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 <iostream>
#define mod 1000000007
using namespace std;
int inv[2000005],jc[2000005],jcinv[2000005];
inline int C(int x,int y)
{
	return (long long)jc[x]*jcinv[y]%mod*jcinv[x-y]%mod;
}
inline int cal(int x,int y)
{
	int rtn=0;
	for(int i=1;i<=y+1;i++)
		rtn=(rtn+C(i+x,i))%mod;
	return rtn;
}
int main(int argc, char** argv) {
	inv[1]=jc[0]=jc[1]=jcinv[0]=jcinv[1]=1;
	for(int i=2;i<=2000004;i++)
	{
		jc[i]=(long long)jc[i-1]*i%mod;
		inv[i]=(long long)(mod-mod/i)*inv[mod%i]%mod;
		jcinv[i]=(long long)jcinv[i-1]*inv[i]%mod;
	}
	int a,b,c,d;
	cin >> a >> b >> c >> d;
	cout << ((cal(c,d)-cal(c,b-1)-cal(a-1,d)+cal(a-1,b-1))%mod+mod)%mod;
	return 0;
}