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 ll N = 2e6 + 87;
const ll MOD = 1e9 + 7;
ll f[N], fi[N];
ll c(ll n, ll k)
{
    return f[n] * fi[k] % MOD * fi[n - k] % MOD;
}
int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    f[0] = f[1] = fi[1] = fi[0] = 1;
    for (int i = 2; i < N; ++i) f[i] = i * f[i - 1] % MOD;
    for (int i = 2; i < N; ++i) fi[i] = (MOD - MOD / i) * fi[MOD % i] % MOD; 
    for (int i = 2; i < N; ++i) (fi[i] *= fi[i - 1]) %= MOD;

    ll r1, c1, r2, c2, ans = 0;
    cin >> r1 >> c1 >> r2 >> c2;
    for (ll i = r1; i <= r2; ++i)
        ans += c(c2 + i + 1, i + 1) - c(c1 + i,  i + 1);
    cout << (ans % MOD + MOD) % MOD;
}
