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;
typedef long long ll;
const int mod=1e9+7;
const int N=2e6+6;
ll r1,c1,r2,c2;
ll fac[N],infac[N];
ll sq(ll a){
	return (a*a)%mod;
}
ll pw(ll a,ll b){
	if(b==0)return 1;
	if(b==1)return a%mod;
	if(b&1) return (a*sq(pw(a,b>>1)))%mod;
	return sq(pw(a,b>>1))%mod;
}
ll ncr(ll n,ll r){
	if(n==r)return 1;
	if(n<r)return 0;
	ll res=fac[n];
	res*=infac[r];
	res%=mod;
	res*=infac[n-r];
	res%=mod;
	return res;
}
int main(){
	infac[1]=infac[0]=fac[0]=fac[1]=1;
	for(int i=1;i<N;i++){
		fac[i]=fac[i-1]*i;
		fac[i]%=mod;
		infac[i]=pw(fac[i],mod-2);
	}
	cin>>r1>>c1>>r2>>c2;
	ll ans=0;
	for (ll i=c1;i<=c2;i++){
        ll tmp=ncr(r2+i+1,i+1)-ncr(r1+i,i+1);
        tmp+=mod;tmp%=mod;
        ans+=tmp;ans%=mod;
    }
	cout<<ans;
	return 0;
}