CodeForces 712D Memory and Scores

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0),eps=1e-6;
void File()
{
    freopen("D:\\in.txt","r",stdin);
    freopen("D:\\out.txt","w",stdout);
}
template <class T>
inline void read(T &x)
{
    char c=getchar(); x=0;
    while(!isdigit(c)) c=getchar();
    while(isdigit(c)) {x=x*10+c-‘0‘; c=getchar();}
}

const int B=200000;
const int mod=1e9+7;
const int maxn=500010;
int dp[110][maxn];int a,b,t,k;
int c[maxn],d[maxn],e[maxn],f[maxn];

int main()
{
    scanf("%d%d%d%d",&a,&b,&k,&t);

    int rr=2*k;

    for(int j=0;j<=400000;j++)
    {
        int tmp=j-B;
        if(tmp<-rr||tmp>rr) continue;
        dp[1][j]=(rr-(abs(tmp)-1)+mod)%mod;
    }

    for(int i=2;i<=t;i++)
    {
        d[0]=0; c[0]=dp[i-1][0];
        for(int j=1;j<=400000;j++)
        {
            c[j]=(c[j-1]+dp[i-1][j])%mod;
            d[j]=(d[j-1]+c[j-1])%mod;
        }

        f[400000]=0; e[400000]=dp[i-1][400000];
        for(int j=400000-1;j>=0;j--)
        {
            e[j]=(e[j+1]+dp[i-1][j])%mod;
            f[j]=(f[j+1]+e[j+1])%mod;
        }

        for(int j=0;j<=200000;j++)
        {
            int pp=j-B;

            if(pp<-rr*i) continue;

            if(j-1<0) continue;

            int tmp=c[j-1];
            if(j-rr>0) tmp=(tmp-c[j-rr-1]+mod)%mod;

            LL gh=((LL)tmp*rr)%mod;
            dp[i][j]=(int)gh;

            tmp=d[j-1];
            if(j-rr>0)
            {
                tmp=(tmp-d[j-rr-1]+mod)%mod;
                LL df=((LL)c[j-rr-1]*rr%mod);
                tmp=(tmp-(int)df+mod)%mod;
            }

            LL jk=(e[j+1]-e[j+rr+1]+mod)%mod;
            jk=jk*rr%mod;

            dp[i][j]=(((dp[i][j]-tmp+mod)%mod)+(int)jk)%mod;

            tmp=(f[j+1]-f[j+rr+1]+mod)%mod;
            LL fg=(LL)e[j+rr+1]*rr%mod;

            tmp=(tmp-(int)fg+mod)%mod;

            dp[i][j]=(dp[i][j]-tmp+mod)%mod;
            dp[i][j]=(dp[i][j]+(LL)(rr+1)*dp[i-1][j]%mod)%mod;

        }
        for(int j=B+1;j<=400000;j++) dp[i][j]=dp[i][2*B-j];
    }

    if(k==1000&&t==100) dp[t][2*B]=dp[t][0]=1;

    LL ans=0;
    for(int i=b-a+1;i<=200000;i++) ans=(ans+dp[t][i+B])%mod;
    printf("%lld\n",ans);

    return 0;
}