This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }
constexpr int md = 1e9 + 7; constexpr int iv2 = (md + 1) / 2;
inline int add(int a, int b) { a += b; if(a>=md){a-=md;} return a; }
inline int sub(int a, int b) { a -= b; if(a<0){a+=md;} return a; }
inline int mul(int a, int b) { return (ll)a * b % md; }
inline int bp(int a, int n) { int res = 1;
for (; n; n >>= 1, a = mul(a, a)) {
if (n & 1) res = mul(res, a);
} return res;
}
inline int inv(int a) { return bp(a, md - 2); }
const int N = 2e3 + 10;
int f[N], iff[N];
inline void calc() {
f[0] = 1;
for (int i = 1; i < N; ++i) f[i] = mul(f[i - 1], i);
iff[N - 1] = inv(f[N - 1]);
for (int i = N - 2; ~i; --i) iff[i] = mul(iff[i + 1], i + 1);
}
inline int C(int n, int k) {
return mul(f[n], mul(iff[k], iff[n - k]));
}
inline void solve() { calc();
int n, k;
cin >> n >> k;
unordered_map<string,int> mp;
mp.reserve(1024); mp.max_load_factor(0.25);
for (int i = 0; i < n; ++i) {
string s; cin >> s;
sort(all(s));
++mp[s];
}
ve<int> dp(k + 1); dp[0] = 1;
for (auto &[str, cnt] : mp) {
ve<int> f(k + 1);
for (int i = 0; i <= cnt; ++i) {
int c = i * (i - 1) / 2;
for (int s = 0; s + c <= k; ++s) {
f[s + c] = add(f[s + c], mul(dp[s], C(cnt, i)));
}
} dp.swap(f);
}
cout << dp[k];
}
signed main() {
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
int q = 1; // cin >> q;
while (q--) solve();
cerr << fixed << setprecision(3) << "Time execution: " << (double)clock() / CLOCKS_PER_SEC << endl;
}
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