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
//In The Name of Allah
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 2e6 + 10;
const ll mod = 1e9 + 7;

ll fact[N], inv[N];

ll Pow(ll a, ll b){
    ll res = 1;
    for (; b; b = b >> 1)
        res = res * (b & 1 ? a : 1) % mod, a = a * a % mod;
    return res;
}

ll C(ll n, ll m){
    if (m < 0 || n < m)
        return 0;
    return fact[n] * inv[m] % mod * inv[n - m] % mod;
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    ll r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    fact[0] = inv[0] = 1;
    for (ll i = 1; i < N; i ++)
        fact[i] = fact[i - 1] * i % mod, inv[i] = Pow(fact[i], mod - 2);
    ll ans = 0;
    for (ll x = r1; x <= r2; x ++)
        ans = (ans + C(x + c2 + 1, x + 1) - C(x + c1, x + 1)) % mod;
    ans = (ans + mod) % mod;
    cout << ans;
    return 0;
}
