#line 1 "main.cpp"
/**
* @title Template
*/
#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>
#include <stack>
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/container/lazy_propagation_segment_tree.cpp"
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/bit_operation.cpp"
#include <cstddef>
#include <cstdint>
constexpr size_t bit_ppc(const uint64_t x) { return __builtin_popcountll(x); }
constexpr size_t bit_ctzr(const uint64_t x) { return x == 0 ? 64 : __builtin_ctzll(x); }
constexpr size_t bit_ctzl(const uint64_t x) { return x == 0 ? 64 : __builtin_clzll(x); }
constexpr size_t bit_width(const uint64_t x) { return 64 - bit_ctzl(x); }
constexpr uint64_t bit_msb(const uint64_t x) { return x == 0 ? 0 : uint64_t(1) << (bit_width(x) - 1); }
constexpr uint64_t bit_lsb(const uint64_t x) { return x & (-x); }
constexpr uint64_t bit_cover(const uint64_t x) { return x == 0 ? 0 : bit_msb(2 * x - 1); }
constexpr uint64_t bit_rev(uint64_t x) {
x = ((x >> 1) & 0x5555555555555555) | ((x & 0x5555555555555555) << 1);
x = ((x >> 2) & 0x3333333333333333) | ((x & 0x3333333333333333) << 2);
x = ((x >> 4) & 0x0F0F0F0F0F0F0F0F) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
x = ((x >> 8) & 0x00FF00FF00FF00FF) | ((x & 0x00FF00FF00FF00FF) << 8);
x = ((x >> 16) & 0x0000FFFF0000FFFF) | ((x & 0x0000FFFF0000FFFF) << 16);
x = (x >> 32) | (x << 32);
return x;
}
/**
* @title Bit Operations
*/
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/monoid.cpp"
#include <type_traits>
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/other/monoid.cpp"
#include <stdexcept>
template <class T, class = void>
class has_identity: public std::false_type { };
template <class T>
class has_identity<T, typename std::conditional<false, decltype(T::identity()), void>::type>: public std::true_type { };
template <class T>
constexpr typename std::enable_if<has_identity<T>::value, typename T::type>::type empty_exception() {
return T::identity();
}
template <class T>
[[noreturn]] typename std::enable_if<!has_identity<T>::value, typename T::type>::type empty_exception() {
throw std::runtime_error("type T has no identity");
}
template <class T, bool HasIdentity>
class fixed_monoid_impl: public T {
public:
using type = typename T::type;
static constexpr type convert(const type &value) { return value; }
static constexpr type revert(const type &value) { return value; }
template <class Mapping, class Value, class... Args>
static constexpr void operate(Mapping &&func, Value &value, const type &op, Args&&... args) {
value = func(value, op, std::forward<Args>(args)...);
}
template <class Constraint>
static constexpr bool satisfies(Constraint &&func, const type &value) {
return func(value);
}
};
template <class T>
class fixed_monoid_impl<T, false> {
public:
class type {
public:
typename T::type value;
bool state;
explicit constexpr type(): value(typename T::type { }), state(false) { }
explicit constexpr type(const typename T::type &value): value(value), state(true) { }
};
static constexpr type convert(const typename T::type &value) { return type(value); }
static constexpr typename T::type revert(const type &value) {
if (!value.state) throw std::runtime_error("attempted to revert identity to non-monoid");
return value.value;
}
static constexpr type identity() { return type(); }
static constexpr type operation(const type &v1, const type &v2) {
if (!v1.state) return v2;
if (!v2.state) return v1;
return type(T::operation(v1.value, v2.value));
}
template <class Mapping, class Value, class... Args>
static constexpr void operate(Mapping &&func, Value &value, const type &op, Args&&... args) {
if (!op.state) return;
value = func(value, op.value, std::forward<Args>(args)...);
}
template <class Constraint>
static constexpr bool satisfies(Constraint &&func, const type &value) {
if (!value.state) return false;
return func(value.value);
}
};
template <class T>
using fixed_monoid = fixed_monoid_impl<T, has_identity<T>::value>;
/**
* @title Monoid Utility
*/
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/container/lazy_propagation_segment_tree.cpp"
#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/container/lazy_propagation_segment_tree.cpp"
#include <iterator>
#line 11 "/Users/kodamankod/Desktop/cpp_programming/Library/container/lazy_propagation_segment_tree.cpp"
template <class CombinedMonoid>
class lazy_propagation_segment_tree {
public:
using structure = CombinedMonoid;
using value_monoid = typename CombinedMonoid::value_structure;
using operator_monoid = typename CombinedMonoid::operator_structure;
using value_type = typename CombinedMonoid::value_structure::type;
using operator_type = typename CombinedMonoid::operator_structure::type;
using size_type = size_t;
private:
using fixed_operator_monoid = fixed_monoid<operator_monoid>;
using fixed_operator_type = typename fixed_operator_monoid::type;
class node_type {
public:
value_type value;
fixed_operator_type lazy;
node_type(
const value_type &value = value_monoid::identity(),
const fixed_operator_type &lazy = fixed_operator_monoid::identity()
): value(value), lazy(lazy) { }
};
static void S_apply(node_type &node, const fixed_operator_type &op, const size_type length) {
fixed_operator_monoid::operate(structure::operation, node.value, op, length);
node.lazy = fixed_operator_monoid::operation(node.lazy, op);
}
void M_propagate(const size_type index, const size_type length) {
S_apply(M_tree[index << 1 | 0], M_tree[index].lazy, length);
S_apply(M_tree[index << 1 | 1], M_tree[index].lazy, length);
M_tree[index].lazy = fixed_operator_monoid::identity();
}
void M_fix_change(const size_type index) {
M_tree[index].value =
value_monoid::operation(M_tree[index << 1 | 0].value, M_tree[index << 1 | 1].value);
}
void M_pushdown(const size_type index) {
const size_type lsb = bit_ctzr(index);
for (size_type story = bit_width(index); story != lsb; --story) {
M_propagate(index >> story, 1 << (story - 1));
}
}
void M_pullup(size_type index) {
index >>= bit_ctzr(index);
while (index != 1) {
index >>= 1;
M_fix_change(index);
}
}
std::vector<node_type> M_tree;
public:
lazy_propagation_segment_tree() = default;
explicit lazy_propagation_segment_tree(const size_type size) { initialize(size); }
template <class InputIterator>
explicit lazy_propagation_segment_tree(InputIterator first, InputIterator last) { construct(first, last); }
void initialize(const size_type size) {
clear();
M_tree.assign(size << 1, node_type());
}
template <class InputIterator>
void construct(InputIterator first, InputIterator last) {
clear();
const size_type size = std::distance(first, last);
M_tree.reserve(size << 1);
M_tree.assign(size, node_type());
for (; first != last; ++first) {
M_tree.emplace_back(*first, fixed_operator_monoid::identity());
}
for (size_type index = size - 1; index != 0; --index) {
M_fix_change(index);
}
}
value_type fold(size_type first, size_type last) {
assert(first <= last);
assert(last <= size());
first += size();
last += size();
M_pushdown(first);
M_pushdown(last);
value_type fold_l = value_monoid::identity();
value_type fold_r = value_monoid::identity();
while (first != last) {
if (first & 1) {
fold_l = value_monoid::operation(fold_l, M_tree[first].value);
++first;
}
if (last & 1) {
--last;
fold_r = value_monoid::operation(M_tree[last].value, fold_r);
}
first >>= 1;
last >>= 1;
}
return value_monoid::operation(fold_l, fold_r);
}
void operate(size_type first, size_type last, const operator_type &op_) {
assert(first <= last);
assert(last <= size());
const auto op = fixed_operator_monoid::convert(op_);
first += size();
last += size();
M_pushdown(first);
M_pushdown(last);
const size_type first_c = first;
const size_type last_c = last;
for (size_type story = 0; first != last; ++story) {
if (first & 1) {
S_apply(M_tree[first], op, 1 << story);
++first;
}
if (last & 1) {
--last;
S_apply(M_tree[last], op, 1 << story);
}
first >>= 1;
last >>= 1;
}
M_pullup(first_c);
M_pullup(last_c);
}
void assign(size_type index, const value_type &val) {
assert(index < size());
index += size();
for (size_type story = bit_width(index); story != 0; --story) {
M_propagate(index >> story, 1 << (story - 1));
}
M_tree[index].value = val;
M_tree[index].lazy = fixed_operator_monoid::identity();
while (index != 1) {
index >>= 1;
M_fix_change(index);
}
}
template <bool ToRight = true, class Constraint, std::enable_if_t<ToRight>* = nullptr>
size_type satisfies(const size_type left, Constraint &&func) {
assert(left <= size());
if (func(value_monoid::identity())) return left;
size_type first = left + size();
size_type last = 2 * size();
M_pushdown(first);
M_pushdown(last);
const size_type last_c = last;
value_type fold = value_monoid::identity();
const auto try_merge = [&](const size_type index) {
value_type tmp = value_monoid::operation(fold, M_tree[index].value);
if (func(tmp)) return true;
fold = std::move(tmp);
return false;
};
const auto subtree = [&](size_type index, size_type story) {
while (index < size()) {
M_propagate(index, 1 << (story - 1));
index <<= 1;
if (!try_merge(index)) ++index;
--story;
}
return index - size() + 1;
};
size_type story = 0;
while (first < last) {
if (first & 1) {
if (try_merge(first)) return subtree(first, story);
++first;
}
first >>= 1;
last >>= 1;
++story;
}
while (story--) {
last = last_c >> story;
if (last & 1) {
--last;
if (try_merge(last)) return subtree(last, story);
}
}
return size() + 1;
}
template <bool ToRight = true, class Constraint, std::enable_if_t<!ToRight>* = nullptr>
size_type satisfies(const size_type right, Constraint &&func) {
assert(right <= size());
if (func(value_monoid::identity())) return right;
size_type first = size();
size_type last = right + size();
M_pushdown(first);
M_pushdown(last);
const size_type first_c = first;
value_type fold = value_monoid::identity();
const auto try_merge = [&](const size_type index) {
value_type tmp = value_monoid::operation(M_tree[index].value, fold);
if (func(tmp)) return true;
fold = std::move(tmp);
return false;
};
const auto subtree = [&](size_type index, size_type story) {
while (index < size()) {
M_propagate(index, 1 << (story - 1));
index <<= 1;
if (try_merge(index + 1)) ++index;
--story;
}
return index - size();
};
size_type story = 0;
while (first < last) {
if (first & 1) ++first;
if (last & 1) {
--last;
if (try_merge(last)) return subtree(last, story);
}
first >>= 1;
last >>= 1;
++story;
}
const size_type cover = bit_cover(first_c);
while (story--) {
first = (cover >> story) - ((cover - first_c) >> story);
if (first & 1) {
if (try_merge(first)) return subtree(first, story);
}
}
return size_type(-1);
}
void clear() {
M_tree.clear();
M_tree.shrink_to_fit();
}
size_type size() const {
return M_tree.size() >> 1;
}
};
/**
* @title Lazy Propagation Segment Tree
*/
#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fast_io.cpp"
#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fast_io.cpp"
#include <cstring>
#line 7 "/Users/kodamankod/Desktop/cpp_programming/Library/other/fast_io.cpp"
namespace fast_io {
static constexpr size_t buf_size = 1 << 18;
static constexpr size_t buf_margin = 1;
static constexpr size_t block_size = 10000;
static constexpr size_t integer_size = 20;
static char inbuf[buf_size + buf_margin] = {};
static char outbuf[buf_size + buf_margin] = {};
static char block_str[block_size * 4 + buf_margin] = {};
static constexpr uint64_t power10[] = {
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000,
100000000000000, 1000000000000000, 10000000000000000, 100000000000000000,
1000000000000000000, 10000000000000000000u
};
class scanner {
private:
size_t M_in_pos = 0, M_in_end = buf_size;
void M_load() {
M_in_end = fread(inbuf, 1, buf_size, stdin);
inbuf[M_in_end] = '\0';
}
void M_reload() {
size_t length = M_in_end - M_in_pos;
memmove(inbuf, inbuf + M_in_pos, length);
M_in_end = length + fread(inbuf + length, 1, buf_size - length, stdin);
inbuf[M_in_end] = '\0';
M_in_pos = 0;
}
void M_ignore_space() {
while (inbuf[M_in_pos] <= ' ') {
if (__builtin_expect(++M_in_pos == M_in_end, 0)) M_reload();
}
}
char M_next() { return inbuf[M_in_pos++]; }
char M_next_nonspace() {
M_ignore_space();
return inbuf[M_in_pos++];
}
public:
scanner() { M_load(); }
void scan(char &c) { c = M_next_nonspace(); }
void scan(std::string &s) {
M_ignore_space();
s = "";
do {
size_t start = M_in_pos;
while (inbuf[M_in_pos] > ' ') ++M_in_pos;
s += std::string(inbuf + start, inbuf + M_in_pos);
if (inbuf[M_in_pos] != '\0') break;
M_reload();
} while (true);
}
template <class T>
typename std::enable_if<std::is_integral<T>::value, void>::type scan(T &x) {
char c = M_next_nonspace();
if (__builtin_expect(M_in_pos + integer_size >= M_in_end, 0)) M_reload();
bool n = false;
if (c == '-') n = true, x = 0;
else x = c & 15;
while ((c = M_next()) >= '0') x = x * 10 + (c & 15);
if (n) x = -x;
}
template <class T, class... Args>
void scan(T &x, Args&... args) {
scan(x); scan(args...);
}
template <class T>
scanner& operator >> (T &x) {
scan(x); return *this;
}
};
class printer {
private:
size_t M_out_pos = 0;
void M_flush() {
fwrite(outbuf, 1, M_out_pos, stdout);
M_out_pos = 0;
}
void M_precompute() {
for (size_t i = 0; i < block_size; ++i) {
size_t j = 4, k = i;
while (j--) {
block_str[i * 4 + j] = k % 10 + '0';
k /= 10;
}
}
}
static constexpr size_t S_integer_digits(uint64_t n) {
if (n >= power10[10]) {
if (n >= power10[19]) return 20;
if (n >= power10[18]) return 19;
if (n >= power10[17]) return 18;
if (n >= power10[16]) return 17;
if (n >= power10[15]) return 16;
if (n >= power10[14]) return 15;
if (n >= power10[13]) return 14;
if (n >= power10[12]) return 13;
if (n >= power10[11]) return 12;
return 11;
}
else {
if (n >= power10[9]) return 10;
if (n >= power10[8]) return 9;
if (n >= power10[7]) return 8;
if (n >= power10[6]) return 7;
if (n >= power10[5]) return 6;
if (n >= power10[4]) return 5;
if (n >= power10[3]) return 4;
if (n >= power10[2]) return 3;
if (n >= power10[1]) return 2;
return 1;
}
}
public:
printer() { M_precompute(); }
~printer() { M_flush(); }
void print(char c) {
outbuf[M_out_pos++] = c;
if (__builtin_expect(M_out_pos == buf_size, 0)) M_flush();
}
void print(const char *s) {
while (*s != 0) {
outbuf[M_out_pos++] = *s++;
if (M_out_pos == buf_size) M_flush();
}
}
void print(const std::string &s) {
for (auto c: s) {
outbuf[M_out_pos++] = c;
if (M_out_pos == buf_size) M_flush();
}
}
template <class T>
typename std::enable_if<std::is_integral<T>::value, void>::type print(T x) {
if (__builtin_expect(M_out_pos + integer_size >= buf_size, 0)) M_flush();
if (x < 0) print('-'), x = -x;
size_t digit = S_integer_digits(x);
size_t len = digit;
while (len >= 4) {
len -= 4;
memcpy(outbuf + M_out_pos + len, block_str + (x % block_size) * 4, 4);
x /= 10000;
}
memcpy(outbuf + M_out_pos, block_str + x * 4 + 4 - len, len);
M_out_pos += digit;
}
template <class T, class... Args>
void print(const T &x, const Args&... args) {
print(x); print(' '); print(args...);
}
template <class... Args>
void println(const Args&... args) {
print(args...); print('\n');
}
template <class T>
printer& operator << (const T &x) {
print(x); return *this;
}
};
};
/**
* @title Fast Input/Output
*/
#line 17 "main.cpp"
template <class T>
using Vec = std::vector<T>;
struct lst_monoid {
struct value_structure {
using type = long long;
static type identity() { return 0; }
static type operation(const type& v1, const type& v2) {
return v1 + v2;
}
};
struct operator_structure {
using type = long long;
static type identity() { return 0; }
static type operation(const type& v1, const type& v2) {
return v1 + v2;
}
};
static typename value_structure::type operation(
const typename value_structure::type &val,
const typename operator_structure::type &op,
const size_t length = 1) {
return val + op * (long long) length;
}
};
fast_io::scanner cin;
fast_io::printer cout;
template <class T>
T scan() {
T x;
cin.scan(x);
return x;
}
int S[200000];
int left[200000];
int right[200000];
Vec<std::pair<int, int>> add1[200000];
Vec<std::pair<int, int>> add2[200000];
Vec<int> query[200000];
long long ans[200000];
int main() {
const auto N = scan<int>();
const auto Q = scan<int>();
for (int i = 0; i < N; ++i) {
S[i] = scan<int>();
}
{
std::stack<std::pair<int, int>> st;
st.emplace(1000000005, 0);
for (int i = 0; i < N; ++i) {
while (st.top().first < S[i]) {
st.pop();
}
left[i] = st.top().second;
st.emplace(S[i], i + N);
}
}
{
std::stack<std::pair<int, int>> st;
st.emplace(1000000005, 2 * N);
for (int i = N - 1; i >= 0; --i) {
while (st.top().first <= S[i]) {
st.pop();
}
right[i] = st.top().second;
st.emplace(S[i], i + N);
}
}
Vec<int> T(Q), L(Q), R(Q);
for (int i = 0; i < Q; ++i) {
T[i] = std::min(scan<int>(), N - 1);
L[i] = scan<int>() + N - 1;
R[i] = scan<int>() + N;
}
const auto add_triangle = [&](const int l, const int r, const int x) {
add1[0].emplace_back(l, x);
add2[0].emplace_back(r, -x);
const auto t = r - l;
if (t < N) {
add1[t].emplace_back(l, -x);
add2[t].emplace_back(r, x);
}
};
for (int i = 0; i < N; ++i) {
add_triangle(left[i] + 1, right[i], S[i]);
add_triangle(left[i] + 1, i + N, -S[i]);
add_triangle(i + N + 1, right[i], -S[i]);
}
for (int i = 0; i < Q; ++i) {
query[T[i]].emplace_back(i);
}
lazy_propagation_segment_tree<lst_monoid> seg1(2 * N), seg2(2 * N);
Vec<long long> ans(Q);
for (int i = 0; i < N; ++i) {
for (const auto [l, x]: add1[i]) {
seg1.operate(l, 2 * N, x);
}
for (const auto [l, x]: add2[i]) {
seg2.operate(l, 2 * N, x);
}
for (const auto k: query[i]) {
ans[k] += seg1.fold(L[k] - i, R[k] - i);
ans[k] += seg2.fold(L[k], R[k]);
}
}
for (int i = 0; i < Q; ++i) {
cout.println(ans[i]);
}
return 0;
}
