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>
#define ll long long
#define loop(n) for(ll i = 0; i<n; i++)
#define sort(a) sort(a.begin(), a.end())
using namespace std;

const int m = 1e6, M = 1e9+7;
ll inverse[3*m], fact[3*m], invfact[3*m];

ll nCr(ll n, ll r){
    ll ans = fact[n]*invfact[r]%M;
    ans = ans*invfact[n-r]%M;
  	return ans;
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0);
    
    inverse[1] = 1;
    for(ll i = 2; i<3*m; i++) inverse[i] = M - M/i * inverse[M%i]%M;
    fact[0] = invfact[0] = 1;
    for(ll i = 1; i<3*m; i++){
        fact[i] = fact[i-1]*i%M;
        invfact[i] = invfact[i-1]*inverse[i]%M;
    }

    ll r1, c1, r2, c2;
    cin>>r1>>c1>>r2>>c2;
    ll ans = nCr(r2+c2+2, c2+1)%M;
    ans = (ans - nCr(r1+c2+1, c2+1))%M;
    ans = (ans - nCr(r2+c1+1, c1))%M;
    ans = (ans + nCr(r1+c1, c1))%M;
    ans = (ans + M)%M;
    cout<<ans<<"\n";
    return 0;
}