#include <iostream>
#include <vector>
using namespace std;
typedef long long ll;
int main()
{
ios_base::sync_with_stdio(0);
ll n, m, MOD;
cin >> n >> m >> MOD;
if (n == 1)
{
cout << (m * (m - 1) / 2 + m) % MOD;
return 0;
}
vector< vector<ll> > dpD1(2, vector<ll>(m));
vector< vector<ll> > dpD2(2, vector<ll>(m));
vector< vector<ll> > dpD3(2, vector<ll>(m));
vector< vector<ll> > dpG1(2, vector<ll>(m));
vector< vector<ll> > dpG2(2, vector<ll>(m));
vector< vector<ll> > dpG3(2, vector<ll>(m));
for (int i = 0; i < m; ++i)
{
dpD1[0][i] = (i + 1) % MOD;
dpG1[0][i] = (m - i) % MOD;
}
dpD2[0][0] = dpD1[0][0];
for (int i = 1; i < m; ++i)
dpD2[0][i] = (dpD2[0][i - 1] + dpD1[0][i]) % MOD;
dpG2[0][m - 1] = dpG1[0][m - 1];
for (int i = m - 2; i >= 0; --i)
dpG2[0][i] = (dpG2[0][i + 1] + dpG1[0][i]) % MOD;
dpD3[0][0] = dpD2[0][0];
for (int i = 1; i < m; ++i)
dpD3[0][i] = (dpD3[0][i - 1] + dpD2[0][i]) % MOD;
dpG3[0][m - 1] = dpG2[0][m - 1];
for (int i = m - 2; i >= 0; --i)
dpG3[0][i] = (dpG3[0][i + 1] + dpG2[0][i]) % MOD;
for (ll i = 1; i < n; ++i)
{
int akt = i % 2;
int pop = akt ^ 1;
for (ll j = 0; j < m; ++j)
{
ll W = dpD2[pop][m - 1];
ll G = 0;
if (j != m - 1)
G = dpG2[pop][j + 1];
ll D = 0;
if (j != 0)
D = dpD3[pop][j - 1];
ll wyn = W * (j + 1) % MOD;
wyn -= G * (j + 1) % MOD;
if (wyn < 0)
wyn += MOD;
wyn -= D;
if (wyn < 0)
wyn += MOD;
dpD1[akt][j] = wyn;
D = 0;
if (j != 0)
D = dpD2[pop][j - 1];
G = 0;
if (j != m - 1)
G = dpG3[pop][j + 1];
wyn = W * (m - j) % MOD;
wyn -= D * (m - j) % MOD;
if (wyn < 0)
wyn += MOD;
wyn -= G;
if (wyn < 0)
wyn += MOD;
dpG1[akt][j] = wyn;
}
dpD2[akt][0] = dpD1[akt][0];
for (int j = 1; j < m; ++j)
dpD2[akt][j] = (dpD2[akt][j - 1] + dpD1[akt][j]) % MOD;
dpD3[akt][0] = dpD2[akt][0];
for (int j = 1; j < m; ++j)
dpD3[akt][j] = (dpD3[akt][j - 1] + dpD2[akt][j]) % MOD;
dpG2[akt][m - 1] = dpG1[akt][m - 1];
for (int j = m - 2; j >= 0; --j)
dpG2[akt][j] = (dpG2[akt][j + 1] + dpG1[akt][j]) % MOD;
dpG3[akt][m - 1] = dpG2[akt][m - 1];
for (int j = m - 2; j >= 0; --j)
dpG3[akt][j] = (dpG3[akt][j + 1] + dpG2[akt][j]) % MOD;
}
cout << dpD2[(n - 1) % 2][m - 1];
return 0;
}
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 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | #include <iostream> #include <vector> using namespace std; typedef long long ll; int main() { ios_base::sync_with_stdio(0); ll n, m, MOD; cin >> n >> m >> MOD; if (n == 1) { cout << (m * (m - 1) / 2 + m) % MOD; return 0; } vector< vector<ll> > dpD1(2, vector<ll>(m)); vector< vector<ll> > dpD2(2, vector<ll>(m)); vector< vector<ll> > dpD3(2, vector<ll>(m)); vector< vector<ll> > dpG1(2, vector<ll>(m)); vector< vector<ll> > dpG2(2, vector<ll>(m)); vector< vector<ll> > dpG3(2, vector<ll>(m)); for (int i = 0; i < m; ++i) { dpD1[0][i] = (i + 1) % MOD; dpG1[0][i] = (m - i) % MOD; } dpD2[0][0] = dpD1[0][0]; for (int i = 1; i < m; ++i) dpD2[0][i] = (dpD2[0][i - 1] + dpD1[0][i]) % MOD; dpG2[0][m - 1] = dpG1[0][m - 1]; for (int i = m - 2; i >= 0; --i) dpG2[0][i] = (dpG2[0][i + 1] + dpG1[0][i]) % MOD; dpD3[0][0] = dpD2[0][0]; for (int i = 1; i < m; ++i) dpD3[0][i] = (dpD3[0][i - 1] + dpD2[0][i]) % MOD; dpG3[0][m - 1] = dpG2[0][m - 1]; for (int i = m - 2; i >= 0; --i) dpG3[0][i] = (dpG3[0][i + 1] + dpG2[0][i]) % MOD; for (ll i = 1; i < n; ++i) { int akt = i % 2; int pop = akt ^ 1; for (ll j = 0; j < m; ++j) { ll W = dpD2[pop][m - 1]; ll G = 0; if (j != m - 1) G = dpG2[pop][j + 1]; ll D = 0; if (j != 0) D = dpD3[pop][j - 1]; ll wyn = W * (j + 1) % MOD; wyn -= G * (j + 1) % MOD; if (wyn < 0) wyn += MOD; wyn -= D; if (wyn < 0) wyn += MOD; dpD1[akt][j] = wyn; D = 0; if (j != 0) D = dpD2[pop][j - 1]; G = 0; if (j != m - 1) G = dpG3[pop][j + 1]; wyn = W * (m - j) % MOD; wyn -= D * (m - j) % MOD; if (wyn < 0) wyn += MOD; wyn -= G; if (wyn < 0) wyn += MOD; dpG1[akt][j] = wyn; } dpD2[akt][0] = dpD1[akt][0]; for (int j = 1; j < m; ++j) dpD2[akt][j] = (dpD2[akt][j - 1] + dpD1[akt][j]) % MOD; dpD3[akt][0] = dpD2[akt][0]; for (int j = 1; j < m; ++j) dpD3[akt][j] = (dpD3[akt][j - 1] + dpD2[akt][j]) % MOD; dpG2[akt][m - 1] = dpG1[akt][m - 1]; for (int j = m - 2; j >= 0; --j) dpG2[akt][j] = (dpG2[akt][j + 1] + dpG1[akt][j]) % MOD; dpG3[akt][m - 1] = dpG2[akt][m - 1]; for (int j = m - 2; j >= 0; --j) dpG3[akt][j] = (dpG3[akt][j + 1] + dpG2[akt][j]) % MOD; } cout << dpD2[(n - 1) % 2][m - 1]; return 0; } |
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