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>
//F6編譯，右上三角形執行，ctrl+c強制停止執行  F5開啟exe
#define ll long long
#define maxn 2000005
#define mod 1000000007
using namespace std;

typedef pair<int, int> P;

ll power(ll a, ll k)
{
    ll res = 1;
    while (k)
    {
        if (k & 1)
            res = res * a % mod;
        a = a * a % mod;
        k /= 2;
    }
    return res;
}
ll inv(ll k) { return power(k, mod - 2); }

ll fac[maxn];

ll cal(ll r, ll c)
{ //C(r+c+2,r+1)
    r++, c++;
    return (fac[r + c] * inv(fac[r] * fac[c] % mod) % mod + mod - 1) % mod;
}

int main()
{
    fac[0] = 1;
    for (int i = 1; i < maxn; i++)
        fac[i] = fac[i - 1] * i % mod;
    ll r1, r2, c1, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    ll ans = cal(r2, c2);
    ans = (ans - cal(r1 - 1, c2) + mod) % mod;
    ans = (ans - cal(r2, c1 - 1) + mod) % mod;
    ans = (ans + cal(r1 - 1, c1 - 1)) % mod;
    cout << ans << endl;

    return 0;
}
