CF479E Riding in a Lift (dp)

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
using namespace std;
typedef long long ll;
const int N=1e6+10;
const int mod=1e9+7;
ll f[5010][5010];
ll sum[5050];
int main(){
    int n,a,b,k;
    cin>>n>>a>>b>>k;
    int i,j;
    memset(f,0,sizeof f);
    f[0][a]=1;
    for(i=a;i<=n;i++)
        sum[i]=1;
    int sign;
    if(a<b){
        for(i=1;i<=k;i++){
            for(j=1;j<b;j++){
                int sign1=j+b>>1;
                while(b-sign1<=sign1-j)
                    sign1--;
                f[i][j]=(sum[sign1]-f[i-1][j])%mod;
            }
            sum[0]=0;
            for(int x=1;x<b;x++)
                sum[x]=sum[x-1]+f[i][x];
        }
        int ans=0;
        for(i=1;i<b;i++){
            ans=(ans+f[k][i])%mod;
        }
        cout<<ans<<endl;
    }
    else{
        for(i=1;i<=k;i++){
            for(j=b+1;j<=n;j++){
                int sign1=b+j>>1;
                while(sign1-b<=j-sign1)
                    sign1++;
                f[i][j]=(sum[n]-sum[sign1-1]-f[i-1][j])%mod;
            }
            sum[0]=0;
             for(int x=b+1;x<=n;x++)
                sum[x]=sum[x-1]+f[i][x];
        }
        int ans=0;
        for(i=b+1;i<=n;i++)
            ans=(ans+f[k][i])%mod;
        cout<<ans<<endl;
    }
}