#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
int fstTrue(function<bool(int)> f, int lo, int hi) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
int mid = (lo+hi)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << ts(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
/**
* Description: modular arithmetic operations
* Source:
* KACTL
* https://codeforces.com/blog/entry/63903
* https://codeforces.com/contest/1261/submission/65632855 (tourist)
* https://codeforces.com/contest/1264/submission/66344993 (ksun)
* Verification:
* https://open.kattis.com/problems/modulararithmetic
*/
struct mi {
typedef decay<decltype(MOD)>::type T;
/// don't silently convert to T
T v; explicit operator T() const { return v; }
mi() { v = 0; }
mi(ll _v) {
v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
if (v < 0) v += MOD;
}
friend bool operator==(const mi& a, const mi& b) {
return a.v == b.v; }
friend bool operator!=(const mi& a, const mi& b) {
return !(a == b); }
friend bool operator<(const mi& a, const mi& b) {
return a.v < b.v; }
friend void re(mi& a) { ll x; re(x); a = mi(x); }
friend str ts(mi a) { return ts(a.v); }
mi& operator+=(const mi& m) {
if ((v += m.v) >= MOD) v -= MOD;
return *this; }
mi& operator-=(const mi& m) {
if ((v -= m.v) < 0) v += MOD;
return *this; }
mi& operator*=(const mi& m) {
v = (ll)v*m.v%MOD; return *this; }
mi& operator/=(const mi& m) { return (*this) *= inv(m); }
friend mi pow(mi a, ll p) {
mi ans = 1; assert(p >= 0);
for (; p; p /= 2, a *= a) if (p&1) ans *= a;
return ans;
}
friend mi inv(const mi& a) { assert(a.v != 0);
return pow(a,MOD-2); }
mi operator-() const { return mi(-v); }
mi& operator++() { return *this += 1; }
mi& operator--() { return *this -= 1; }
friend mi operator+(mi a, const mi& b) { return a += b; }
friend mi operator-(mi a, const mi& b) { return a -= b; }
friend mi operator*(mi a, const mi& b) { return a *= b; }
friend mi operator/(mi a, const mi& b) { return a /= b; }
};
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;
vector<vmi> scmb; // small combinations
void genComb(int SZ) {
scmb.assign(SZ,vmi(SZ)); scmb[0][0] = 1;
FOR(i,1,SZ) F0R(j,i+1)
scmb[i][j] = scmb[i-1][j]+(j?scmb[i-1][j-1]:0);
}
/**
* Description: pre-compute factorial mod inverses,
* assumes $MOD$ is prime and $SZ < MOD$.
* Time: O(SZ)
* Source: KACTL
* Verification: https://dmoj.ca/problem/tle17c4p5
*/
vi invs, fac, ifac;
void genFac(int SZ) {
invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ);
invs[1] = fac[0] = ifac[0] = 1;
FOR(i,2,SZ) invs[i] = MOD-(ll)MOD/i*invs[MOD%i]%MOD;
FOR(i,1,SZ) {
fac[i] = (ll)fac[i-1]*i%MOD;
ifac[i] = (ll)ifac[i-1]*invs[i]%MOD;
}
}
mi comb(int a, int b) {
if (a < b || b < 0) return 0;
return mi((ll)fac[a]*ifac[b]%MOD*ifac[a-b]%MOD);
}
int N, L;
int A[105];
mi dp[2][2][105][1005]; //number of components, total weight so far
mi ndp[2][2][105][1005];
void update(int s1, int s2, int j, int newval, mi ways){
//dbg(s1, s2, j, newval, ways);
if(s1 > 1) return;
if(s2 > 1) return;
if(j < 0) return;
if(newval > L){
//if(ways != 0) dbg(s1, s2, j, newval, ways);
return;
}
if(newval < 0) return;
if(ways != mi(0)) assert(newval >= 0);
ndp[s1][s2][j][newval]+=ways;
}
void transition(int i, int s1, int s2, int j, int k){
//dbg(i, s1, s2, j, k);
mi ways = dp[s1][s2][j][k];
if(ways == 0) return;
int newval = k-A[i]*(s1+s2+2*(j));
// if(i == 2 && s1 == 1 && s2 == 0 && j == 0 && k == 1){
// dbg(newval, ways);
// dbg(newval-A[i+1]+A[i+1]*(s1+s2+1+j-1));
// }
// if(i == 2 && s1 == 0 && s2 == 1 && j == 0 && k == 1){
// dbg(newval, ways);
// dbg(newval-A[i+1]+A[i+1]*(s1+1+s2+2*(j)));
// }
//start a new middle component
update(s1, s2, j+1, newval-2*A[i+1]+A[i+1]*(s1+s2+2*(j+1)), ways);
//add to an existing middle component
update(s1, s2, j, newval+A[i+1]*(s1+s2+2*(j)), ways*j*2);
//join together two middle components
update(s1, s2, j-1, newval+2*A[i+1]+A[i+1]*(s1+s2+2*(j-1)), ways*comb(j, 2)*2);
//join left and middle components
if(s1 == 1) update(s1, s2, j-1, newval+2*A[i+1]+A[i+1]*(s1+s2+2*(j-1)), ways*j);
//join middle and right components
if(s2 == 1) update(s1, s2, j-1, newval+2*A[i+1]+A[i+1]*(s1+s2+2*(j-1)), ways*j);
//add to an existing left component
if(s1 == 1) update(s1, s2, j, newval+A[i+1]*(s1+s2+2*(j)), ways);
//add to an existing right component
if(s2 == 1) update(s1, s2, j, newval+A[i+1]*(s1+s2+2*(j)), ways);
//start a left component
update(s1+1, s2, j, newval-A[i+1]+A[i+1]*(s1+1+s2+2*(j)), ways);
//start a right component
update(s1, s2+1, j, newval-A[i+1]+A[i+1]*(s1+s2+1+2*(j)), ways);
//transform a middle component into a left component
update(s1+1, s2, j-1, newval+A[i+1]+A[i+1]*(s1+1+s2+2*(j-1)), ways*j);
//transform a middle component into a right component
update(s1, s2+1, j-1, newval+A[i+1]+A[i+1]*(s1+s2+1+2*(j-1)), ways*j);
}
int main() {
setIO();
cin >> N >> L;
genFac(205);
if(N == 1){
ps(1);
return 0;
}
for(int i = 1; i <= N; i++){
cin >> A[i];
}
sort(A+1, A+1+N);
dp[1][0][0][0] = 1;
dp[0][1][0][0] = 1;
dp[0][0][1][0] = 1;
for(int i = 1; i+1 <= N-1; i++){ //place i+1th building
for(int s1 = 0; s1 < 2; s1++){ //left present
for(int s2 = 0; s2 < 2; s2++){ // right present
for(int j = 0; j <= N; j++){ //middle components
for(int k = 0; k <= L; k++){ //current weight
transition(i, s1, s2, j, k);
}
}
}
}
//move to dp, reset ndp
for(int s1 = 0; s1 < 2; s1++){ //left present
for(int s2 = 0; s2 < 2; s2++){ // right present
for(int j = 0; j <= N; j++){ //middle components
for(int k = 0; k <= L; k++){ //current weight
dp[s1][s2][j][k] = ndp[s1][s2][j][k];
ndp[s1][s2][j][k] = 0;
}
}
}
}
// if(i+1 == 2){
// dbg(dp[1][0][0][1]);
// dbg(dp[0][1][0][1]);
// }
}
//dbg(dp[1][1][0][4]);
mi ans = 0;
//for answer, we could put N on the sides or the middle
for(int k = 0; k <= L; k++){
int newval = k-A[N-1]+A[N];
mi ways = dp[0][1][0][k]; //N on the left
if(newval <= L){
//if(ways != 0) dbg(k, ways, "Ans1");
ans+=ways;
}
newval = k-A[N-1]+A[N];
ways = dp[1][0][0][k]; //N on the right
if(newval <= L){
//if(ways != 0) dbg(k, ways, "Ans2");
ans+=ways;
}
newval = k-2*A[N-1]+2*A[N];
ways = dp[1][1][0][k];
if(newval <= L){
//if(ways != 0) dbg(k, ways, "Ans3");
ans+=ways;
}
}
ps(ans);
// you should actually read the stuff at the bottom
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
*/
Compilation message
skyscraper.cpp: In function 'void setIn(std::__cxx11::string)':
skyscraper.cpp:128:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~
skyscraper.cpp: In function 'void setOut(std::__cxx11::string)':
skyscraper.cpp:129:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 2 |
Correct |
6 ms |
3712 KB |
Output is correct |
| 3 |
Correct |
6 ms |
3584 KB |
Output is correct |
| 4 |
Correct |
6 ms |
3584 KB |
Output is correct |
| 5 |
Correct |
8 ms |
3584 KB |
Output is correct |
| 6 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 7 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 8 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 9 |
Correct |
8 ms |
3712 KB |
Output is correct |
| 10 |
Correct |
8 ms |
3712 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
3712 KB |
Output is correct |
| 2 |
Correct |
7 ms |
3712 KB |
Output is correct |
| 3 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 4 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 5 |
Correct |
8 ms |
3584 KB |
Output is correct |
| 6 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 7 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 8 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 9 |
Correct |
8 ms |
3712 KB |
Output is correct |
| 10 |
Correct |
7 ms |
3584 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 2 |
Correct |
6 ms |
3712 KB |
Output is correct |
| 3 |
Correct |
6 ms |
3584 KB |
Output is correct |
| 4 |
Correct |
6 ms |
3584 KB |
Output is correct |
| 5 |
Correct |
8 ms |
3584 KB |
Output is correct |
| 6 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 7 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 8 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 9 |
Correct |
8 ms |
3712 KB |
Output is correct |
| 10 |
Correct |
8 ms |
3712 KB |
Output is correct |
| 11 |
Correct |
7 ms |
3712 KB |
Output is correct |
| 12 |
Correct |
7 ms |
3712 KB |
Output is correct |
| 13 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 14 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 15 |
Correct |
8 ms |
3584 KB |
Output is correct |
| 16 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 17 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 18 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 19 |
Correct |
8 ms |
3712 KB |
Output is correct |
| 20 |
Correct |
7 ms |
3584 KB |
Output is correct |
| 21 |
Correct |
9 ms |
3840 KB |
Output is correct |
| 22 |
Correct |
272 ms |
3704 KB |
Output is correct |
| 23 |
Correct |
235 ms |
3708 KB |
Output is correct |
| 24 |
Correct |
215 ms |
3584 KB |
Output is correct |
| 25 |
Correct |
249 ms |
3584 KB |
Output is correct |
| 26 |
Correct |
217 ms |
3584 KB |
Output is correct |
| 27 |
Correct |
91 ms |
3584 KB |
Output is correct |
| 28 |
Correct |
119 ms |
3712 KB |
Output is correct |
| 29 |
Correct |
213 ms |
3704 KB |
Output is correct |
| 30 |
Correct |
249 ms |
3584 KB |
Output is correct |
