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>
using namespace std;
const long long N = 1e4 + 5, mod = 1e9 + 7;
long long fac[N], inv[N];
long long n, l;
long long fp(long long base, long long power)
{
long long ret = 1;
while (power)
{
if (power & 1)
ret = (ret * base) % mod;
power >>= 1;
base = (base * base) % mod;
}
return ret;
}
long long ncr(long long nn, long long rr)
{
if (rr > nn || rr < 0)
return 0;
return ((fac[nn] * inv[rr]) % mod * inv[nn - rr]) % mod;
}
int main()
{
ios_base::sync_with_stdio(0), cin.tie(NULL), cout.tie(NULL);
cin >> n >> l;
vector<pair<int, long long>> arr(n);
for (int i = 0; i < n; i++)
cin >> arr[i].first, arr[i].second = i;
fac[0] = fac[1] = 1;
for (long long i = 2; i <= l; i++)
fac[i] = (i * fac[i - 1]) % mod;
inv[l] = fp(fac[l], mod - 2);
for (long long i = l - 1; i >= 0; i--)
inv[i] = (inv[i + 1] * (i + 1)) % mod;
sort(arr.begin(), arr.end());
long long ans = 0;
if (arr[0].first == arr[n - 1].first)
return (ncr(l - (n - 1) * arr[0].first, l - n - (n - 1) * arr[0].first) * fac[n]) % mod;
do
{
int boxes = l - n;
for (int i = 1; i < n; i++)
boxes -= max(arr[i - 1].first - 1, arr[i].first - 1);
ans = (ans + ncr(n + boxes, boxes)) % mod;
} while (next_permutation(arr.begin(), arr.end()));
cout << ans << "\n";
}
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