Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

* f(r,c) :=  (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)



Given are integers r_1, r_2, c_1, and c_2. Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

* 1 ≤ r_1 ≤ r_2 ≤ 10^6
* 1 ≤ c_1 ≤ c_2 ≤ 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


r_1 c_1 r_2 c_2


Output

Print the sum of f(i, j) modulo (10^9+7).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
#include <bits/stdc++.h>
using namespace std;
const long long mod=1e+9+7;
long long qpow(long long p,long long q) {
    long long r=1;
    for(;q;p*=p,p%=mod,q>>=1){
    	if(q&1){
    		r*=p,r%=mod;
		}
	}
    return r;
}
long long inv(long long p) {
    return qpow(p,mod-2);
}
const long long N = 1e+6+5;
int f[N],g[N];
int solve(long long i,long long m) {
    memset(f,0,sizeof f);
    memset(g,0,sizeof g);
    g[0]=i+1; 
	f[1]=i+1;
    for(int k=2;k<=m+1;k++){
    	f[k]=f[k-1]*(i+k)%mod*inv(k)%mod;
	}
    for(int j=1;j<=m;j++){
    	g[j]=(g[j-1]+f[j+1])%mod;
	}
    return g[m];
}
signed main(){
    int r1,c1,r2,c2;
    cin>>r1>>c1>>r2>>c2;
    --r1; 
	--c1;
    cout<<((solve(r2,c2)-solve(r1,c2)-solve(r2,c1)+solve(r1,c1)%mod+mod)%mod);
    return 0;
}