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;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<n;i++)
#define all(v) v.begin(),v.end()
#define inf (int)(3e18)
#define P pair<int,int>
#define mod (int)(1e9+7)

template<class T>inline void chmin(T &a,T b){a=min(a,b);}
template<class T>inline void chmax(T &a,T b){a=max(a,b);}

int perm[2000005];
void init(){
	perm[0]=1;
	REP(i,2000005)perm[i]=perm[i-1]*i%mod;
}
int mod_pow(int x,int y){
	int res=1;
	while(y){
		if(y&1)res*=x;
		res%=mod;
		x=x*x%mod;
		y>>=1;
	}
	return res;
}
int comb(int x,int y){
	return perm[x]*mod_pow(perm[x-y],mod-2)%mod*mod_pow(perm[y],mod-2)%mod;
}
signed main(){
	init();
	int r1,c1,r2,c2;cin>>r1>>c1>>r2>>c2;
	int ans=0;
	for(int i=r1;i<=r2;i++){
		int ans1=comb(i+c2+1,i+1);
		int ans2=comb(i+c1,i+1);
		ans+=(ans1-ans2+mod)%mod;
		ans%=mod;
	}
	cout<<ans<<endl;
}
