LOJ #2109. 「JLOI2015」骗我呢 数形结合+组合+容斥

神仙题！！！！       

其实还是有一点没有搞懂，但是大体上差不多懂了.   

code:   

#include <bits/stdc++.h>     
#define ll long long 
#define N 3200020  
#define setIO(s) freopen(s".in","r",stdin) 
using namespace std;
const int mod=1e9+7;    
int n,m;     
ll fac[N],inv[N];   
void Init() 
{
    fac[0]=fac[1]=inv[0]=inv[1]=1;      
    int i,j;  
    for(i=2;i<N;++i)   
    {
        fac[i]=(ll)i*fac[i-1]%mod;   
        inv[i]=(mod-mod/i)*inv[mod%i]%mod;   
    }
    for(i=1;i<N;++i)    
        inv[i]=inv[i]*inv[i-1]%mod;    
} 
ll C(int x,int y) 
{
    if(x<y||x<0||y<0)   
        return 0;     
    return fac[x]*inv[y]%mod*inv[x-y]%mod;   
}
ll calc(int x,int y) 
{
    if(x<0||y<0)   
        return 0;   
    return C(x+y,y);  
}
void turn_A(int &x,int &y) 
{
    swap(x,y);   
    x--,y++;  
}
void turn_B(int &x,int &y) 
{
    swap(x,y);   
    x+=m+2,y-=m+2;   
}
ll ans; 
int main() 
{ 
    // setIO("input");    
    int i,j;      
    scanf("%d%d",&n,&m);      
    Init();     
    ans=calc(n+m+1,n);    
    int x=n+m+1,y=n;    
    while(x>=0&&y>=0) 
    {
        turn_A(x,y),ans=(ans-calc(x,y)+mod)%mod;   
        turn_B(x,y),ans=(ans+calc(x,y)+mod)%mod;   
    }
    x=n+m+1,y=n;    
    while(x>=0&&y>=0) 
    {
        turn_B(x,y),ans=(ans-calc(x,y)+mod)%mod;    
        turn_A(x,y),ans=(ans+calc(x,y)+mod)%mod;      
    }
    printf("%lld\n",ans);  
    return 0; 
}