#pragma GCC optimize("Ofast")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
#define mp make_pair
#define eb emplace_back
#define pb push_back
#define e1 first
#define e2 second
#define uint unsigned int
#define ll long long
#define ull unsigned long long
#define ld long double
#define float long double
#define size(x) (int)x.size()
#define satori int testCases; cin>>testCases; while(testCases--)
#define fastio ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define all(r) begin(r),end(r)
#define time chrono::high_resolution_clock().now().time_since_epoch().count()
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 rng(chrono::high_resolution_clock().now().time_since_epoch().count());
///////////////////
#define debug if(1)
///////////////////
int mul(ll a,ll b,ll mod){
return (a*b)%mod;
}
int32_t main()
{
fastio;
int n,m,mod;
cin>>n>>m>>mod;
vector<vector<int>> l(n,vector<int>(m,0));
vector<vector<int>> r(n,vector<int>(m,0));
for(int j=0;j<m;j++)
l[0][j]=j+1,r[0][j]=m-j;
int ps,pss,tot;
for(int i=1;i<n;i++){
ps=pss=tot=0;
for(int j=0;j<m;j++){
r[i][j]-=mul(ps,m-j,mod);
if(r[i][j]<0)
r[i][j]+=mod;
l[i][j]-=pss;
if(l[i][j]<0)
l[i][j]+=mod;
ps+=l[i-1][j];
if(ps>=mod)
ps-=mod;
pss+=ps;
if(pss>=mod)
pss-=mod;
tot+=l[i-1][j];
if(tot>=mod)
tot-=mod;
}
ps=pss=0;
for(int j=m-1;j>=0;j--){
l[i][j]+=mul(tot,j+1,mod);
if(l[i][j]>=mod)
l[i][j]-=mod;
r[i][j]+=mul(tot,m-j,mod);
if(r[i][j]>=mod)
r[i][j]-=mod;
l[i][j]-=mul(ps,j+1,mod);
if(l[i][j]<0)
l[i][j]+=mod;
r[i][j]-=pss;
if(r[i][j]<0)
r[i][j]+=mod;
ps+=r[i-1][j];
if(ps>=mod)
ps-=mod;
pss+=ps;
if(pss>=mod)
pss-=mod;
}
}
int res=0;
for(int j=0;j<m;j++){
res+=l[n-1][j];
if(res>=mod)
res-=mod;
}
cout<<res<<'\n';
}
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 | #pragma GCC optimize("Ofast") #pragma GCC optimization ("O3") #pragma GCC optimization ("unroll-loops") #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace __gnu_pbds; using namespace std; #define mp make_pair #define eb emplace_back #define pb push_back #define e1 first #define e2 second #define uint unsigned int #define ll long long #define ull unsigned long long #define ld long double #define float long double #define size(x) (int)x.size() #define satori int testCases; cin>>testCases; while(testCases--) #define fastio ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0) #define all(r) begin(r),end(r) #define time chrono::high_resolution_clock().now().time_since_epoch().count() typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> ordered_set; mt19937 rng(chrono::high_resolution_clock().now().time_since_epoch().count()); /////////////////// #define debug if(1) /////////////////// int mul(ll a,ll b,ll mod){ return (a*b)%mod; } int32_t main() { fastio; int n,m,mod; cin>>n>>m>>mod; vector<vector<int>> l(n,vector<int>(m,0)); vector<vector<int>> r(n,vector<int>(m,0)); for(int j=0;j<m;j++) l[0][j]=j+1,r[0][j]=m-j; int ps,pss,tot; for(int i=1;i<n;i++){ ps=pss=tot=0; for(int j=0;j<m;j++){ r[i][j]-=mul(ps,m-j,mod); if(r[i][j]<0) r[i][j]+=mod; l[i][j]-=pss; if(l[i][j]<0) l[i][j]+=mod; ps+=l[i-1][j]; if(ps>=mod) ps-=mod; pss+=ps; if(pss>=mod) pss-=mod; tot+=l[i-1][j]; if(tot>=mod) tot-=mod; } ps=pss=0; for(int j=m-1;j>=0;j--){ l[i][j]+=mul(tot,j+1,mod); if(l[i][j]>=mod) l[i][j]-=mod; r[i][j]+=mul(tot,m-j,mod); if(r[i][j]>=mod) r[i][j]-=mod; l[i][j]-=mul(ps,j+1,mod); if(l[i][j]<0) l[i][j]+=mod; r[i][j]-=pss; if(r[i][j]<0) r[i][j]+=mod; ps+=r[i-1][j]; if(ps>=mod) ps-=mod; pss+=ps; if(pss>=mod) pss-=mod; } } int res=0; for(int j=0;j<m;j++){ res+=l[n-1][j]; if(res>=mod) res-=mod; } cout<<res<<'\n'; } |
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