#include <bits/stdc++.h>
using namespace std;
const int N = 1e7;
int n, m;
long long p;
vector<vector<long long> > d, u;
int main()
{
scanf("%d%d%lld", &n, &m, &p);
d.resize(n + 1);
u.resize(n + 1);
d[0].resize(m + 2);
u[0].resize(m + 2);
d[0][1] = u[0][m] = 1;
for (int i = 1; i <= n; i++) {
d[i].resize(m + 2);
u[i].resize(m + 2);
long long sumup = 0;
for (int j = 1; j <= m; j++) {
sumup = (sumup + d[i - 1][j]) % p;
}
long long all = sumup;
long long sumdown = 0;
long long pref = 0;
for (long long j = 1; j <= m; j++) {
sumup = (sumup - d[i - 1][j] + p) % p;
sumdown = (sumdown + u[i - 1][j - 1]) % p;
pref = (pref + sumdown) % p;
u[i][j] = (j * sumup + pref) % p;
u[i][j] = (j*all - u[i][j] + p) % p;
}
sumdown = 0;
for (int j = 1; j <= m; j++) {
sumdown = (sumdown + u[i - 1][j]) % p;
}
sumup = 0;
pref = 0;
for (long long j = m; j > 0; j--) {
sumdown = (sumdown - u[i - 1][j] + p) % p;
sumup = (sumup + d[i - 1][j + 1]) % p;
pref = (pref + sumup) % p;
d[i][j] = ((long long)(m - j + 1) * sumdown + pref) % p;
d[i][j] = ((long long)(m - j + 1) * all - d[i][j] + p) % p;
}
}
long long res = 0;
for (int i = 1; i <= m; i++) {
res = (res + d[n][i]) % p;
}
printf("%lld\n", res);
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | #include <bits/stdc++.h> using namespace std; const int N = 1e7; int n, m; long long p; vector<vector<long long> > d, u; int main() { scanf("%d%d%lld", &n, &m, &p); d.resize(n + 1); u.resize(n + 1); d[0].resize(m + 2); u[0].resize(m + 2); d[0][1] = u[0][m] = 1; for (int i = 1; i <= n; i++) { d[i].resize(m + 2); u[i].resize(m + 2); long long sumup = 0; for (int j = 1; j <= m; j++) { sumup = (sumup + d[i - 1][j]) % p; } long long all = sumup; long long sumdown = 0; long long pref = 0; for (long long j = 1; j <= m; j++) { sumup = (sumup - d[i - 1][j] + p) % p; sumdown = (sumdown + u[i - 1][j - 1]) % p; pref = (pref + sumdown) % p; u[i][j] = (j * sumup + pref) % p; u[i][j] = (j*all - u[i][j] + p) % p; } sumdown = 0; for (int j = 1; j <= m; j++) { sumdown = (sumdown + u[i - 1][j]) % p; } sumup = 0; pref = 0; for (long long j = m; j > 0; j--) { sumdown = (sumdown - u[i - 1][j] + p) % p; sumup = (sumup + d[i - 1][j + 1]) % p; pref = (pref + sumup) % p; d[i][j] = ((long long)(m - j + 1) * sumdown + pref) % p; d[i][j] = ((long long)(m - j + 1) * all - d[i][j] + p) % p; } } long long res = 0; for (int i = 1; i <= m; i++) { res = (res + d[n][i]) % p; } printf("%lld\n", res); } |
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