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 N=1e5+100;
const ll p=1e9+7;

ll inv(ll a,ll p) { //p为素数,a<p
    if(a==1)return 1;
    return (p-p/a)*inv(p%a,p)%p;
}

ll sum(ll r,ll c){
    if(r<=0||c<=0)return 0;
    if(c==1)return r;
    ll s=0,a=1,b=1;
    for(ll x=1;x<=c-1;++x)
        a=(a*x)%p;
    ll x=2,y=c;
    for(ll i=x;i<=y;++i)
        b=(b*i)%p;
    a=inv(a,p);
    s+=b*a%p;
    ++y;
    while(y<=r+c-1){
        b=b*inv(x++,p)%p;
        b=b*(y++)%p;
        s=(s+b*a)%p;
    }
    return s;
}

int main(){
    ll r1,c1,r2,c2;
    cin>>r1>>c1>>r2>>c2;
    ++r1;++c1;++r2;++c2;
    cout<<(sum(r2,c2)+sum(r1-1,c1-1)-sum(r2,c1-1)-sum(r1-1,c2)+2*p)%p;
    return 0;
}