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 <algorithm>
#include <iostream>
#include <numeric>
#include <vector>
#include <set>
typedef long long llong;
const int MAXN = 300 + 10;
const int MOD = 1e9 + 7;
const int INF = 1e9;
int n, m;
int fact[MAXN];
int var[MAXN][MAXN];
int comb[MAXN][MAXN];
int dp[MAXN][MAXN][MAXN];
bool bl[MAXN][MAXN][MAXN];
int f(int idx, int zeros, int ones)
{
if (idx == 0)
{
return (zeros == 0 && ones == 0);
}
if (bl[idx][zeros][ones])
{
return dp[idx][zeros][ones];
}
bl[idx][zeros][ones] = true;
int len = (2*n - idx + 1) / m + (idx != 1);
for (int addOnes = std::max(0, len - ones) ; addOnes <= std::min(len, zeros) ; ++addOnes)
{
dp[idx][zeros][ones] += (((((1LL * f(idx-1, zeros - addOnes, ones + 2*addOnes - len) * comb[len][addOnes]) % MOD) * var[zeros][addOnes]) % MOD) * var[ones][len - addOnes]) % MOD;
if (dp[idx][zeros][ones] >= MOD) dp[idx][zeros][ones] -= MOD;
}
return dp[idx][zeros][ones];
}
void solve()
{
for (int i = 0 ; i <= n ; ++i)
{
comb[i][0] = 1;
}
fact[0] = 1;
for (int i = 1 ; i <= n ; ++i)
{
fact[i] = (1LL * fact[i-1] * i) % MOD;
}
for (int i = 1 ; i <= n ; ++i)
{
for (int j = 1 ; j <= i ; ++j)
{
comb[i][j] = comb[i-1][j] + comb[i-1][j-1];
if (comb[i][j] >= MOD) comb[i][j] -= MOD;
}
}
for (int i = 0 ; i <= n ; ++i)
{
for (int j = 0 ; j <= i ; ++j)
{
var[i][j] = (1LL * comb[i][j] * fact[j]) % MOD;
}
}
int ans = f(m, n, 0);
for (int i = 1 ; i <= n ; ++i)
{
ans *= 2;
ans %= MOD;
}
std::cout << ans << '\n';
}
void read()
{
std::cin >> n >> m;
}
void fastIO()
{
std::ios_base :: sync_with_stdio(0);
std::cout.tie(nullptr);
std::cin.tie(nullptr);
}
int main()
{
fastIO();
read();
solve();
return 0;
}
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