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 maxn = 2e6 + 5;
const ll mod = 1e9 + 7;
ll fac[maxn];
void init() {
    fac[0] = 1;
    for (int i = 1; i < maxn; ++i)
        fac[i] = fac[i - 1] * i % mod;
}
ll modpow(ll base, ll power) {
    ll res = 1;
    while (power) {
        if (power & 1) res = res * base % mod;
        base = base * base % mod;
        power >>= 1;
    }
    return res;
}
int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    init();
    int r1, c1, r2, c2; cin >> r1 >> c1 >> r2 >> c2;
    ll ans = 0;
    for (int i = r1; i <= r2; ++i)
        ans = (ans + ((fac[i + c2 + 1] * modpow(fac[i + 1], mod - 2) % mod * modpow(fac[c2], mod - 2) % mod) - 
            (fac[i + c1] * modpow(fac[i + 1], mod - 2) % mod * modpow(fac[c1 - 1], mod - 2) % mod) + mod) % mod) % mod;
    cout << ans << '\n';
    return 0;
}