#include<iostream>
#include<vector>
#define mp make_pair
#define fi first
#define se second
using namespace std;
const int N = 1e7;
vector<long long>v[N];
vector<long long>super_pref[N];
long long prev_wrong;
int n, m;
long long mod;
long long good_per_one() {
long long res = 0;
for (int i = 1; i <= m; i++) {
res += i;
res %= mod;
}
return res;
}
void add_super_pref(int i) {
long long pref = 0;
for (int j = 0; j < m; j++) {
pref += v[i][j];
pref %= mod;
super_pref[i].push_back(pref);
}
}
int main() {
ios_base::sync_with_stdio(0);
cin >> n >> m >> mod;
const long long single = good_per_one();
for (int i = 0; i < m; i++) {
v[0].push_back(i + 1);
if (i > 0) {
v[0].back() += v[0][i - 1];
v[0].back() %= mod;
}
}
long long all = single;
for (int i = 1; i < n; i++) {
add_super_pref(i - 1);
long long curr_wrong = 0;
for (int j = 0; j < m; j++) {
long long bad = (prev_wrong * (j + 1)) % mod;
if (m - j - 2 >= 0) {
bad += (v[i - 1][m - j - 2] * (j + 1)) % mod;
bad %= mod;
}
if (j > 0) {
bad += super_pref[i - 1][j - 1];
bad %= mod;
}
curr_wrong += bad;
curr_wrong %= mod;
v[i].push_back(((all * (j + 1) % mod) - bad + mod) % mod);
if (j > 0) {
v[i].back() += v[i][j - 1];
v[i].back() %= mod;
}
}
all *= single;
all %= mod;
prev_wrong = curr_wrong;
}
cout << v[n - 1].back() << endl;
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 | #include<iostream> #include<vector> #define mp make_pair #define fi first #define se second using namespace std; const int N = 1e7; vector<long long>v[N]; vector<long long>super_pref[N]; long long prev_wrong; int n, m; long long mod; long long good_per_one() { long long res = 0; for (int i = 1; i <= m; i++) { res += i; res %= mod; } return res; } void add_super_pref(int i) { long long pref = 0; for (int j = 0; j < m; j++) { pref += v[i][j]; pref %= mod; super_pref[i].push_back(pref); } } int main() { ios_base::sync_with_stdio(0); cin >> n >> m >> mod; const long long single = good_per_one(); for (int i = 0; i < m; i++) { v[0].push_back(i + 1); if (i > 0) { v[0].back() += v[0][i - 1]; v[0].back() %= mod; } } long long all = single; for (int i = 1; i < n; i++) { add_super_pref(i - 1); long long curr_wrong = 0; for (int j = 0; j < m; j++) { long long bad = (prev_wrong * (j + 1)) % mod; if (m - j - 2 >= 0) { bad += (v[i - 1][m - j - 2] * (j + 1)) % mod; bad %= mod; } if (j > 0) { bad += super_pref[i - 1][j - 1]; bad %= mod; } curr_wrong += bad; curr_wrong %= mod; v[i].push_back(((all * (j + 1) % mod) - bad + mod) % mod); if (j > 0) { v[i].back() += v[i][j - 1]; v[i].back() %= mod; } } all *= single; all %= mod; prev_wrong = curr_wrong; } cout << v[n - 1].back() << endl; return 0; } |
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