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<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include<cctype>
#include<cassert>
#define REP(i,a,b) for(register int i=(a); i<(b); i++)
#define REPE(i,a,b) for(register int i=(a); i<=(b); i++)
using namespace std;
typedef long long ll;
#define MAXN 1000007
#define MO 1000000007
ll fz[MAXN*2],fm[MAXN*2];
ll g(int r, int c) {
	ll ans=0;
	REPE(i,0,r) {
		ans=(ans+fz[i+1+c]*fm[i+1]%MO*fm[c]%MO)%MO;
	}
	return ans;
}
int qpow(ll a, int b) {
	ll ans=1;
	for(;b;b>>=1) {
		if(b&1) ans=ans*a%MO;
		a=a*a%MO;
	}
	return ans;
}
int main() {
	int r1,c1,r2,c2; scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
	fz[0]=fz[1]=1;
	fm[0]=fm[1]=1;
	REP(i,2,MAXN*2) fz[i]=fz[i-1]*i%MO;
	REP(i,2,MAXN*2) fm[i]=qpow(fz[i],MO-2);
	printf("%lld\n", (g(r2,c2)-g(r2,c1-1)-g(r1-1,c2)+g(r1-1,c1-1)+MO*2)%MO);
}

