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 mod = 1e+9 + 7;

ll r1, r2, c1, c2;

ll qPow(ll a, ll b)
{
    a %= mod;
    
    ll res = 1;
    while(b) {
        if(b & 1) res = res * a % mod;
        a = a * a % mod, b >>= 1;
    }
    return res;
}

ll C(ll n, ll m)
{
    if(n < m) return 0;
    
    ll res = 1;
    for(int i = 1; i <= m; ++i)
        res = res * (n - i + 1) % mod * qPow(i, mod - 2) % mod;
    return res;
}

int main()
{
    scanf("%lld%lld%lld%lld", &r1, &c1, &r2, &c2);
    
    ++r2, ++c2;
    printf("%lld", ((C(r2 + c2, c2) - C(r1 + c2, c2) - C(r2 + c1, c1) + C(r1 + c1, c1)) % mod + mod) % mod);
}