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
#pragma GCC optimize("Ofast,unroll-loops")
#include<bits/stdc++.h>
#define int long long
#define F first
#define S second
#define P pair
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define rep(i,a,b) for(int i=a;i<b;i++)
#define V vector
#define RE return
#define ALL(a) a.begin(),a.end()
#define MP make_pair
#define PB push_back
#define PF push_front
#define FILL(a,b) memset(a,b,sizeof(a))
using namespace std;
int inv[1000005],mod=1e9+7;
int c(int x,int y){
	int t=x+1,sum=t;
	FOR(i,2,y+1){
		t=t*(x+i)%mod*inv[i]%mod;
		sum=(sum+t)%mod;
	}
	RE sum;
}
signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	inv[1]=1;
	FOR(i,2,1000001)inv[i]=mod-inv[mod%i]*(mod/i)%mod;
	int c1,c2,r1,r2;
	cin>>r1>>c1>>r2>>c2;
	cout<<(c(c2,r2)-c(c1-1,r2)-c(c2,r1-1)+c(c1-1,r1-1)+2*mod)%mod;
	RE 0;
}

