/*
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,fma,bmi,bmi2,sse4.2,popcnt,lzcnt")
*/
#include <bits/stdc++.h>
#define taskname ""
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define i64 long long
#define isz(x) (int)x.size()
using namespace std;
template<class data_t, data_t _mod>
struct modular_fixed_base{
#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)
static_assert(IS_UNSIGNED(data_t));
static_assert(_mod >= 1);
static constexpr bool VARIATE_MOD_FLAG = false;
static constexpr data_t mod(){
return _mod;
}
template<class T>
static vector<modular_fixed_base> precalc_power(T base, int SZ){
vector<modular_fixed_base> res(SZ + 1, 1);
for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;
return res;
}
static vector<modular_fixed_base> _INV;
static void precalc_inverse(int SZ){
if(_INV.empty()) _INV.assign(2, 1);
for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);
}
// _mod must be a prime
static modular_fixed_base _primitive_root;
static modular_fixed_base primitive_root(){
if(_primitive_root) return _primitive_root;
if(_mod == 2) return _primitive_root = 1;
if(_mod == 998244353) return _primitive_root = 3;
data_t divs[20] = {};
divs[0] = 2;
int cnt = 1;
data_t x = (_mod - 1) / 2;
while(x % 2 == 0) x /= 2;
for(auto i = 3; 1LL * i * i <= x; i += 2){
if(x % i == 0){
divs[cnt ++] = i;
while(x % i == 0) x /= i;
}
}
if(x > 1) divs[cnt ++] = x;
for(auto g = 2; ; ++ g){
bool ok = true;
for(auto i = 0; i < cnt; ++ i){
if(modular_fixed_base(g).power((_mod - 1) / divs[i]) == 1){
ok = false;
break;
}
}
if(ok) return _primitive_root = g;
}
}
constexpr modular_fixed_base(){ }
modular_fixed_base(const double &x){ data = _normalize(llround(x)); }
modular_fixed_base(const long double &x){ data = _normalize(llround(x)); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){
int sign = x >= 0 ? 1 : -1;
data_t v = _mod <= sign * x ? sign * x % _mod : sign * x;
if(sign == -1 && v) v = _mod - v;
return v;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data; }
modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }
modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
modular_fixed_base &operator++(){ return *this += 1; }
modular_fixed_base &operator--(){ return *this += _mod - 1; }
modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }
modular_fixed_base &operator*=(const modular_fixed_base &rhs){
if constexpr(is_same_v<data_t, unsigned int>) data = (unsigned long long)data * rhs.data % _mod;
else if constexpr(is_same_v<data_t, unsigned long long>){
long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data);
data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);
}
else data = _normalize(data * rhs.data);
return *this;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base &inplace_power(T e){
if(e == 0) return *this = 1;
if(data == 0) return *this = {};
if(data == 1 || e == 1) return *this;
if(data == mod() - 1) return e % 2 ? *this : *this = -*this;
if(e < 0) *this = 1 / *this, e = -e;
if(e == 1) return *this;
modular_fixed_base res = 1;
for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;
return *this = res;
}
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
modular_fixed_base power(T e) const{
return modular_fixed_base(*this).inplace_power(e);
}
modular_fixed_base &operator/=(const modular_fixed_base &otr){
make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;
if(a < _INV.size()) return *this *= _INV[a];
while(a){
make_signed_t<data_t> t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return *this *= u;
}
#define ARITHMETIC_OP(op, apply_op)\
modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }
ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)
#undef ARITHMETIC_OP
#define COMPARE_OP(op)\
bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\
template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\
friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; }
COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
friend istream &operator>>(istream &in, modular_fixed_base &number){
long long x;
in >> x;
number.data = modular_fixed_base::_normalize(x);
return in;
}
//#define _SHOW_FRACTION
friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
out << number.data;
#if defined(LOCAL) && defined(_SHOW_FRACTION)
cerr << "(";
for(auto d = 1; ; ++ d){
if((number * d).data <= 1000000){
cerr << (number * d).data;
if(d != 1) cerr << "/" << d;
break;
}
else if((-number * d).data <= 1000000){
cerr << "-" << (-number * d).data;
if(d != 1) cerr << "/" << d;
break;
}
}
cerr << ")";
#endif
return out;
}
data_t data = 0;
#undef _SHOW_FRACTION
#undef IS_INTEGRAL
#undef IS_UNSIGNED
};
template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;
template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;
const unsigned int mod = (119 << 23) + 1; // 998244353
// const unsigned int mod = 1e9 + 7; // 1000000007
// const unsigned int mod = 1e9 + 9; // 1000000009
// const unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;
// Requires modular
template<class modular_t, class len_t, bool ALLOW_BINEXP>
struct hash_base{
#ifdef LOCAL
#define ASSERT(c) assert(c)
#else
#define ASSERT(c) 42
#endif
static modular_t _base, _inv_base;
template<class T = int>
static void setup(T base = 0){
if constexpr(modular_t::VARIATE_MOD_FLAG) modular_t::setup((unsigned long long)1e18 + 9);
if(!base) base = mt19937(chrono::high_resolution_clock::now().time_since_epoch().count())() % 100'000'000 + 100'000'000;
_base = base, _inv_base = modular_t(1) / base;
}
static vector<modular_t> _power, _inv_power;
static void setup_power(size_t len){
if(_power.empty()) _power.push_back(1), _inv_power.push_back(1);
while((int)_power.size() <= len){
_power.push_back(_power.back() * _base);
_inv_power.push_back(_inv_power.back() * _inv_base);
}
}
static modular_t power(len_t e){
assert(e >= 0);
if constexpr(ALLOW_BINEXP) return e < (int)_power.size() ? _power[e] : _base.power(e);
else{
if((int)_power.size() <= e) setup_power(e);
return _power[e];
}
}
static modular_t inv_power(len_t e){
assert(e >= 0);
if constexpr(ALLOW_BINEXP) return e < (int)_inv_power.size() ? _inv_power[e] : _inv_base.power(e);
else{
if((int)_power.size() <= e) setup_power(e);
return _inv_power[e];
}
}
hash_base(){ ASSERT(_base >= 1); }
hash_base(const modular_t &x, len_t len): data(x), len(len){ ASSERT(_base >= 1); }
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
hash_base(T x): data(x), len(1){ ASSERT(_base >= 1); }
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
hash_base(const vector<T> &s){
ASSERT(_base >= 1);
for(auto c: s) *this += hash_base(c);
}
hash_base(const string &s){
ASSERT(_base >= 1);
for(auto c: s) *this += hash_base(c);
}
hash_base &operator=(const hash_base &x){
data = x.data, len = x.len;
return *this;
}
hash_base &operator+=(const hash_base &x){
data = power(x.len) * data + x.data;
len += x.len;
return *this;
}
hash_base operator+(const hash_base &x) const{ return hash_base(*this) += x; }
hash_base &inplace_append_right(const hash_base &x){ return *this += x; }
hash_base append_right(const hash_base &x) const{ return hash_base(*this).inplace_append_right(x); }
hash_base &inplace_append_left(const hash_base &x){
data += power(len) * x.data;
len += x.len;
return *this;
}
hash_base append_left(const hash_base &x) const{ return hash_base(*this).inplace_append_left(x); }
hash_base &inplace_pop_right(const hash_base &x){
assert(len >= x.len);
data = inv_power(x.len) * (data - x.data);
len -= x.len;
return *this;
}
hash_base pop_right(const hash_base &x) const{ return hash_base(*this).inplace_pop_right(x); }
hash_base &inplace_pop_left(const hash_base &x){
assert(len >= x.len);
data -= power(len - x.len) * x.data;
len -= x.len;
return *this;
}
hash_base pop_left(const hash_base &x) const{ return hash_base(*this).inplace_pop_left(x); }
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
hash_base &inplace_update(len_t pos, T x){
assert(0 <= pos && pos < len);
data += power(len - pos - 1) * x;
return *this;
}
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
hash_base update(len_t pos, T x) const{ return hash_base(*this).inplace_update(pos, x); }
hash_base &inplace_update(len_t pos, const hash_base &x){
assert(0 <= pos && pos + x.len <= len);
data += power(len - pos - x.len) * x.data;
return *this;
}
hash_base update(len_t pos, const hash_base &x) const{ return hash_base(*this).inplace_update(pos, x); }
#define COMPARE_OP(op)\
bool operator op(const hash_base &x) const{ return data op x.data; }
COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)
#undef COMPARE_OP
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
hash_base &operator*=(T x){
assert(x >= 0);
if(x == 0) return *this = {};
if(x == 1) return *this;
hash_base res{};
for(auto e = x; e; e >>= 1){
if(e & 1) res += *this;
*this += *this;
}
return *this = res;
}
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
hash_base operator*(T x) const{ return hash_base(*this) *= x; }
template<class T, typename enable_if<is_integral_v<T>>::type* = nullptr>
friend hash_base operator*(T x, const hash_base &h){ return hash_base(h) *= x; }
friend ostream &operator<<(ostream &out, const hash_base &x){ return out << "{" << x.data << ", " << x.len << "}"; }
modular_t data = 0;
len_t len = 0;
#undef ASSERT
};
template<class modular_t, class len_t, bool ALLOW_BINEXP> modular_t hash_base<modular_t, len_t, ALLOW_BINEXP>::_base;
template<class modular_t, class len_t, bool ALLOW_BINEXP> modular_t hash_base<modular_t, len_t, ALLOW_BINEXP>::_inv_base;
template<class modular_t, class len_t, bool ALLOW_BINEXP> vector<modular_t> hash_base<modular_t, len_t, ALLOW_BINEXP>::_power{1};
template<class modular_t, class len_t, bool ALLOW_BINEXP> vector<modular_t> hash_base<modular_t, len_t, ALLOW_BINEXP>::_inv_power{1};
using hash_t = hash_base<modular_fixed_base<unsigned long long, (unsigned long long)1e18 + 9>, int, false>;
template<bool HAS_QUERY, bool HAS_UPDATE, class T, class U, class F1, class F2, class F3>
struct segment_tree_base{
static_assert(HAS_QUERY || HAS_UPDATE);
#define ifQ if constexpr(HAS_QUERY)
#define ifU if constexpr(HAS_UPDATE)
int n, size, log;
vector<T> data;
vector<U> data_action;
F1 TT; // monoid operation (always adjacent)
T T_id; // monoid identity
F2 UU; // monoid operation (superset, subset)
U U_id; // monoid identity
F3 UT; // action of U on T (superset, subset)
// O(n)
segment_tree_base(F1 TT, T T_id, F2 UU, U U_id, F3 UT): TT(TT), T_id(T_id), UU(UU), U_id(U_id), UT(UT){ }
segment_tree_base &operator=(const segment_tree_base &seg){
n = seg.n;
size = seg.size;
log = seg.log;
data = seg.data;
data_action = seg.data_action;
}
// O(1)
friend void swap(segment_tree_base &x, segment_tree_base &y){
swap(x.n, y.n);
swap(x.size, y.size);
swap(x.log, y.log);
swap(x.data, y.data);
swap(x.data_action, y.data_action);
}
// O(n)
void build(int n){
assert(n >= 0);
this->n = n;
size = 1;
while(size < n) size <<= 1;
log = __lg(size);
ifQ data.assign(size << 1, T_id);
ifU data_action.assign(HAS_QUERY ? size : size << 1, U_id);
}
// O(n)
void build(int n, T x){
static_assert(HAS_QUERY);
assert(n >= 0);
this->n = n;
size = 1;
while(size < n) size <<= 1;
log = __lg(size);
data.assign(size << 1, T_id);
fill(data.begin() + size, data.begin() + size + n, x);
for(auto i = size - 1; i >= 1; -- i) refresh(i);
ifU data_action.assign(size, U_id);
}
// O(n)
template<class V>
void build(const vector<V> &a){
static_assert(HAS_QUERY);
n = (int)a.size();
size = 1;
while(size < n) size <<= 1;
log = __lg(size);
data.assign(size << 1, T_id);
copy(a.begin(), a.end(), data.begin() + size);
for(auto i = size - 1; i >= 1; -- i) refresh(i);
ifU data_action.assign(size, U_id);
}
// O(n)
void build_action(int n){
static_assert(!HAS_QUERY && HAS_UPDATE);
assert(n >= 0);
build(n);
}
// O(n)
void build_action(int n, U f){
static_assert(!HAS_QUERY && HAS_UPDATE);
assert(n >= 0);
this->n = n;
size = 1;
while(size < n) size <<= 1;
log = __lg(size);
data_action.assign(size << 1, U_id);
fill(data_action.begin() + size, data_action.begin() + size + n, f);
}
// O(n)
template<class V>
void build_action(const vector<V> &a){
static_assert(!HAS_QUERY && HAS_UPDATE);
n = (int)a.size();
size = 1;
while(size < n) size <<= 1;
log = __lg(size);
data_action.assign(size << 1, U_id);
copy(a.begin(), a.end(), data_action.begin() + size);
}
// O(1)
void refresh(int u){
static_assert(HAS_QUERY);
data[u] = TT(data[u << 1], data[u << 1 | 1]);
}
// O(1)
void apply(int u, U f){
static_assert(HAS_UPDATE);
ifQ data[u] = UT(f, data[u]);
if(!HAS_QUERY || u < size) data_action[u] = UU(f, data_action[u]);
}
// O(1)
void push(int u){
static_assert(HAS_UPDATE);
apply(u << 1, data_action[u]), apply(u << 1 | 1, data_action[u]);
data_action[u] = U_id;
}
// O(log(n)) if HAS_UPDATE, O(1) otherwise.
T query(int p){
static_assert(HAS_QUERY);
assert(0 <= p && p < n);
p += size;
ifU for(auto i = log; i >= 1; -- i) push(p >> i);
return data[p];
}
// O(log(n))
U query_action(int p){
static_assert(!HAS_QUERY && HAS_UPDATE);
assert(0 <= p && p < n);
p += size;
ifU for(auto i = log; i >= 1; -- i) push(p >> i);
return data_action[p];
}
// O(log(n))
T query(int ql, int qr){
static_assert(HAS_QUERY);
assert(0 <= ql && ql <= qr && qr <= n);
if(ql == qr) return T_id;
ql += size, qr += size;
ifU for(auto i = log; i >= 1; -- i){
if(ql >> i << i != ql) push(ql >> i);
if(qr >> i << i != qr) push(qr >> i);
}
T res_left = T_id, res_right = T_id;
for(; ql < qr; ql >>= 1, qr >>= 1){
if(ql & 1) res_left = TT(res_left, data[ql ++]);
if(qr & 1) res_right = TT(data[-- qr], res_right);
}
return TT(res_left, res_right);
}
// O(1)
T query_all() const{
static_assert(HAS_QUERY);
return data[1];
}
// O(n)
vector<T> to_array(){
static_assert(HAS_QUERY);
ifU for(auto u = 1; u < size; ++ u) push(u);
return vector<T>(data.begin() + size, data.begin() + size + n);
}
// O(n)
vector<U> to_array_of_updates(){
static_assert(!HAS_QUERY && HAS_UPDATE);
for(auto u = 1; u < size; ++ u) push(u);
return vector<U>(data_action.begin() + size, data_action.begin() + size + n);
}
// O(log(n))
void set(int p, T x){
static_assert(HAS_QUERY);
assert(0 <= p && p < n);
p += size;
ifU for(auto i = log; i >= 1; -- i) push(p >> i);
data[p] = x;
for(auto i = 1; i <= log; ++ i) refresh(p >> i);
}
// O(log(n))
void set_action(int p, U f){
static_assert(!HAS_QUERY && HAS_UPDATE);
assert(0 <= p && p < n);
p += size;
for(auto i = log; i >= 1; -- i) push(p >> i);
data_action[p] = f;
}
// O(log(n))
void update(int p, U f){
static_assert(HAS_UPDATE);
assert(0 <= p && p < n);
p += size;
for(auto i = log; i >= 1; -- i) push(p >> i);
ifQ{
data[p] = UT(f, data[p]);
for(auto i = 1; i <= log; ++ i) refresh(p >> i);
}
else data_action[p] = UU(f, data_action[p]);
}
// O(log(n))
void update(int ql, int qr, U f){
static_assert(HAS_UPDATE);
assert(0 <= ql && ql <= qr && qr <= n);
if(ql == qr) return;
ql += size, qr += size;
for(auto i = log; i >= 1; -- i){
if(ql >> i << i != ql) push(ql >> i);
if(qr >> i << i != qr) push(qr >> i);
}
int _ql = ql, _qr = qr;
for(; ql < qr; ql >>= 1, qr >>= 1){
if(ql & 1) apply(ql ++, f);
if(qr & 1) apply(-- qr, f);
}
ql = _ql, qr = _qr;
ifQ for(auto i = 1; i <= log; ++ i){
if(ql >> i << i != ql) refresh(ql >> i);
if(qr >> i << i != qr) refresh(qr >> i);
}
}
void update_beats(int ql, int qr, auto exit_rule, auto enter_rule, auto update_rule){
static_assert(HAS_QUERY && HAS_UPDATE);
assert(0 <= ql && ql <= qr && qr <= n);
if(ql == qr) return;
ql += size, qr += size;
for(auto i = log; i >= 1; -- i){
if(ql >> i << i != ql) push(ql >> i);
if(qr >> i << i != qr) push(qr >> i);
}
auto recurse = [&](auto self, int u)->void{
if(exit_rule(data[u])) return;
if(enter_rule(data[u])){
apply(u, update_rule(data[u]));
return;
}
push(u);
self(self, u << 1), self(self, u << 1 | 1);
refresh(u);
};
int _ql = ql, _qr = qr;
for(; ql < qr; ql >>= 1, qr >>= 1){
if(ql & 1) recurse(recurse, ql ++);
if(qr & 1) recurse(recurse, -- qr);
}
ql = _ql, qr = _qr;
for(auto i = 1; i <= log; ++ i){
if(ql >> i << i != ql) refresh(ql >> i);
if(qr >> i << i != qr) refresh(qr >> i);
}
}
// pred(sum[ql, r)) is T, T, ..., T, F, F, ..., F
// Returns max r with T
// O(log(n))
int max_pref(int ql, auto pred){
static_assert(HAS_QUERY);
assert(0 <= ql && ql <= n && pred(T_id));
if(ql == n) return n;
ql += size;
ifU for(auto i = log; i >= 1; -- i) push(ql >> i);
T sum = T_id;
do{
while(~ql & 1) ql >>= 1;
if(!pred(TT(sum, data[ql]))){
while(ql < size){
ifU push(ql);
ql = ql << 1;
if(pred(TT(sum, data[ql]))) sum = TT(sum, data[ql ++]);
}
return ql - size;
}
sum = TT(sum, data[ql]);
++ ql;
}while((ql & -ql) != ql);
return n;
}
// pred(sum[l, qr)) is F, F, ..., F, T, T, ..., T
// Returns min l with T
// O(log(n))
int min_suff(int qr, auto pred){
static_assert(HAS_QUERY);
assert(0 <= qr && qr <= n && pred(T_id));
if(qr == 0) return 0;
qr += size;
ifU for(auto i = log; i >= 1; -- i) push(qr - 1 >> i);
T sum = T_id;
do{
-- qr;
while(qr > 1 && qr & 1) qr >>= 1;
if(!pred(TT(data[qr], sum))){
while(qr < size){
ifU push(qr);
qr = qr << 1 | 1;
if(pred(TT(data[qr], sum))) sum = TT(data[qr --], sum);
}
return qr + 1 - size;
}
sum = TT(data[qr], sum);
}while((qr & -qr) != qr);
return 0;
}
template<class output_stream>
friend output_stream &operator<<(output_stream &out, segment_tree_base<HAS_QUERY, HAS_UPDATE, T, U, F1, F2, F3> seg){
out << "{";
for(auto i = 0; i < seg.n; ++ i){
ifQ out << seg.query(i);
else out << seg.query_action(i);
if(i != seg.n - 1) out << ", ";
}
return out << '}';
}
#undef ifQ
#undef ifU
};
// Supports query
template<class T, class F>
auto make_Q_segment_tree(F TT, T T_id){
using U = int;
auto _UU = [&](U, U)->U{ return U{}; };
auto _UT = [&](U, T)->T{ return T{}; };
return segment_tree_base<true, false, T, U, F, decltype(_UU), decltype(_UT)>(TT, T_id, _UU, U{}, _UT);
}
// Supports update
template<class U, class F>
auto make_U_segment_tree(F UU, U U_id){
using T = int;
auto _TT = [&](T, T)->T{ return T{}; };
auto _UT = [&](U, T)->T{ return T{}; };
return segment_tree_base<false, true, T, U, decltype(_TT), F, decltype(_UT)>(_TT, T{}, UU, U_id, _UT);
}
// Supports query and update
template<class T, class U, class F1, class F2, class F3>
auto make_QU_segment_tree(F1 TT, T T_id, F2 UU, U U_id, F3 UT){
return segment_tree_base<true, true, T, U, F1, F2, F3>(TT, T_id, UU, U_id, UT);
}
struct node {
hash_t val;
int lx = -1, rx = -1;
node() {}
node(int val) : lx(val), rx(val) {}
};
void solve() {
int m, n;
cin >> m >> n;
hash_t::setup();
hash_t sigma;
vector<int> a(m), b(n);
for (int i = 0; i < m; ++i) {
cin >> a[i];
if (i) sigma.inplace_append_right(a[i] - a[i - 1]);
}
for (int i = 0; i < n; ++i) {
cin >> b[i];
}
vector<int> aidx(n);
iota(all(aidx), 0);
sort(all(aidx), [&](int x, int y) {
return b[x] < b[y];
});
vector<int> nidx(n);
for (int i = 0; i < n; ++i) nidx[aidx[i]] = i;
auto TT = [&](const auto &lhs, const auto &rhs) {
if (lhs.rx == -1) return rhs;
if (rhs.lx == -1) return lhs;
node res = lhs;
res.val.inplace_append_right(rhs.lx - lhs.rx);
res.val.inplace_append_right(rhs.val);
res.lx = lhs.lx, res.rx = rhs.rx;
return res;
};
auto st = make_Q_segment_tree(TT, node());
st.build(n);
vector<int> res;
for (int i = 0; i < m; ++i) {
st.set(nidx[i], node(i));
}
if (st.query_all().val == sigma) {
res.emplace_back(0);
}
for (int i = m; i < n; ++i) {
st.set(nidx[i], node(i));
st.set(nidx[i - m], node());
if (st.query_all().val == sigma) {
res.emplace_back(i - m + 1);
}
}
cout << isz(res) << "\n";
for (auto val : res) {
cout << val + 1 << " ";
}
cout << "\n";
}
signed main() {
#ifndef CDuongg
if (fopen(taskname".inp", "r"))
assert(freopen(taskname".inp", "r", stdin)), assert(freopen(taskname".out", "w", stdout));
#else
freopen("bai3.inp", "r", stdin);
freopen("bai3.out", "w", stdout);
auto start = chrono::high_resolution_clock::now();
#endif
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1; //cin >> t;
while(t--) solve();
#ifdef CDuongg
auto end = chrono::high_resolution_clock::now();
cout << "\n"; for(int i = 1; i <= 100; ++i) cout << '=';
cout << "\nExecution time: " << chrono::duration_cast<chrono::milliseconds> (end - start).count() << "[ms]" << endl;
#endif
}
