This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// IN THE NAME OF GOD
#include<bits/stdc++.h>
#define endl '\n'
#define file_reading freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
#define flush cout.flush();
using namespace std;
typedef long long ll;
typedef long double dll;
typedef unsigned long long ull;
const ll N = 2e3 + 2, mod = 1e9+7, mod0 = 1e9+7, base0 = 73, mod1 = 998244353, base1 = 89;
vector<pair<ll,ll>> having;
vector<ll> cnt;
string s;
ll dp[N][N], c[N][N];
ll power(ll a, ll b){
if (b == 0) return 1;
ll c = power(a,b/2);
return c*c%mod * (b&1 ? a : 1) % mod;
}
void hashing(){
sort(s.begin(),s.end());
ll ans0 = 0, ans1 = 0;
for(char c : s){
ans0 = ans0 * base0 % mod0 + (c-'a'+1); ans0 %= mod0;
ans1 = ans1 * base1 % mod1 + (c-'a'+1); ans1 %= mod1;
}
having.push_back({ans0,ans1});
}
void cmaking(){
c[0][0] = 1;
for(int i=1; i<N; i++) for(int j=0; j<N; j++) c[i][j] = (j == 0 ? 1 : c[i-1][j] + c[i-1][j-1]), c[i][j] %= mod;
}
void solve(){
cmaking();
int n,k; cin >> n >> k;
for(int i=0; i<n; i++) cin >> s, hashing();
sort(having.begin(),having.end());
cnt.push_back(1);
for(int i=1; i<int(having.size()); i++){
if (having[i].first == having[i-1].first && having[i].second == having[i-1].second) cnt.back()++;
else cnt.push_back(1);
}
dp[0][0] = 1;
for(int i=1; i<=int(cnt.size()); i++){
for(int j=0; j<=k; j++){
for(int taking = 0; taking <= cnt[i-1]; taking++){
if (c[taking][2] > j) break;
dp[i][j] = dp[i][j] + dp[i-1][j-c[taking][2]] * c[cnt[i-1]][taking] % mod; dp[i][j] %= mod;
}
}
}
cout << dp[int(cnt.size())][k] << endl;
}
int32_t main(){
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
int t; t=1; //cin >> t;
while(t--){solve();}
}
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