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Submission #857098

# Submission time Handle Problem Language Result Execution time Memory
857098 2023-10-05T11:30:41 Z alexdd NoM (RMI21_nom) C++17
100 / 100
 78 ms 31828 KB 
#include<bits/stdc++.h>
using namespace std;
#define int long long
const int MOD = 1e9+7;
int n,m;
int dp[2005][2005];
int cntr[2005];
int pref[2005];
int fact[10005];
int invf[5005];
int put2[5005];
int put(int a, int exp)
{
    if(exp==0)
        return 1;
    if(exp%2==0)
        return put((a*a)%MOD,exp/2);
    else
        return (put((a*a)%MOD,exp/2)*a)%MOD;
}
int comb(int x, int y)
{
    if(x<y)
        return 0;
    return ((((fact[x]*invf[y])%MOD)*invf[x-y])%MOD);
}
signed main()
{
    cin>>n>>m;
    for(int i=1;i<=2*n;i++)
        cntr[i%m+1]++;
    fact[0]=1;
    put2[0]=1;
    for(int i=1;i<=5001;i++)
    {
        fact[i]=(fact[i-1]*i)%MOD;
        put2[i]=(put2[i-1]*2LL)%MOD;
    }
    invf[5001] = put(fact[5001], MOD-2);
    for(int i=5000;i>=0;i--)
        invf[i]=(invf[i+1]*(i+1))%MOD;
    dp[0][0]=1;
    for(int i=1;i<=m;i++)
    {
        pref[i]=(pref[i-1]+cntr[i])%MOD;
        for(int cntp=0;cntp<=pref[i]/2;cntp++)
        {
            dp[i][cntp]=0;
            for(int x=0;x<=min(cntp,cntr[i]);x++)
            {
                dp[i][cntp] += (((((dp[i-1][cntp-x] * fact[cntr[i]])%MOD) * comb(pref[i-1] - 2*(cntp-x), x))%MOD) * (put2[cntr[i]-x] * comb(n - (pref[i-1] - 2*(cntp-x) - x) - (cntp-x) - x, cntr[i]-x)%MOD))%MOD;
                dp[i][cntp] %= MOD;
            }
            //cout<<i<<" "<<cntp<<"  "<<dp[i][cntp]<<"\n";
        }
    }
    cout<<dp[m][n];
    return 0;
}
/**

dp[i][cntp] = numarul de moduri de a plasa pietre pe primele i resturi a.i. sa fi plasat cntp perechi de pietre
cntr[i] = nr de pozitii cu restul i
pref[i] = sum(cntr[x]), x = 1..i
dp[i][cntp] = sum(dp[i-1][cntp-x] * fact[cntr[i]] * comb(pref[i-1] - 2*cntp, x) * comb(n - (pref[i-1] - 2*cntp - x) - cntp - x, cntr[i]-x)


*/

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 2396 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2392 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 2396 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2392 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct
21 Correct 1 ms 2396 KB Output is correct
22 Correct 2 ms 4444 KB Output is correct
23 Correct 1 ms 2396 KB Output is correct
24 Correct 2 ms 4444 KB Output is correct
25 Correct 2 ms 4444 KB Output is correct
26 Correct 1 ms 2396 KB Output is correct
27 Correct 3 ms 6488 KB Output is correct

Subtask #4
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 2396 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2392 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct
21 Correct 1 ms 2396 KB Output is correct
22 Correct 2 ms 4444 KB Output is correct
23 Correct 1 ms 2396 KB Output is correct
24 Correct 2 ms 4444 KB Output is correct
25 Correct 2 ms 4444 KB Output is correct
26 Correct 1 ms 2396 KB Output is correct
27 Correct 3 ms 6488 KB Output is correct
28 Correct 5 ms 2396 KB Output is correct
29 Correct 8 ms 6724 KB Output is correct
30 Correct 9 ms 10588 KB Output is correct
31 Correct 5 ms 2396 KB Output is correct
32 Correct 8 ms 6724 KB Output is correct
33 Correct 12 ms 10588 KB Output is correct
34 Correct 18 ms 14932 KB Output is correct

Subtask #5
48.0 / 48.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2392 KB Output is correct
2 Correct 1 ms 2396 KB Output is correct
3 Correct 1 ms 2392 KB Output is correct
4 Correct 1 ms 2396 KB Output is correct
5 Correct 1 ms 2396 KB Output is correct
6 Correct 1 ms 2396 KB Output is correct
7 Correct 1 ms 2396 KB Output is correct
8 Correct 1 ms 2396 KB Output is correct
9 Correct 1 ms 2396 KB Output is correct
10 Correct 1 ms 2396 KB Output is correct
11 Correct 1 ms 2396 KB Output is correct
12 Correct 1 ms 2396 KB Output is correct
13 Correct 1 ms 2396 KB Output is correct
14 Correct 1 ms 2396 KB Output is correct
15 Correct 1 ms 2396 KB Output is correct
16 Correct 1 ms 2396 KB Output is correct
17 Correct 1 ms 2396 KB Output is correct
18 Correct 1 ms 2392 KB Output is correct
19 Correct 1 ms 2396 KB Output is correct
20 Correct 1 ms 2396 KB Output is correct
21 Correct 1 ms 2396 KB Output is correct
22 Correct 2 ms 4444 KB Output is correct
23 Correct 1 ms 2396 KB Output is correct
24 Correct 2 ms 4444 KB Output is correct
25 Correct 2 ms 4444 KB Output is correct
26 Correct 1 ms 2396 KB Output is correct
27 Correct 3 ms 6488 KB Output is correct
28 Correct 5 ms 2396 KB Output is correct
29 Correct 8 ms 6724 KB Output is correct
30 Correct 9 ms 10588 KB Output is correct
31 Correct 5 ms 2396 KB Output is correct
32 Correct 8 ms 6724 KB Output is correct
33 Correct 12 ms 10588 KB Output is correct
34 Correct 18 ms 14932 KB Output is correct
35 Correct 27 ms 2392 KB Output is correct
36 Correct 63 ms 27244 KB Output is correct
37 Correct 30 ms 2396 KB Output is correct
38 Correct 42 ms 14936 KB Output is correct
39 Correct 49 ms 25172 KB Output is correct
40 Correct 78 ms 31828 KB Output is correct