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
mod = 10**9+7
def comb_mod(n,r,mod,invs):
    ans = 1
    for i in range(r):
        ans *= n-i
        ans %= mod
    ans *= invs[r]
    ans %= mod
    return ans

A, B, C, D = map(int, input().split())

invs = [1]*(C+2)
for i in range(1,C+2):
    invs[i] = invs[i-1]*pow(i,mod-2,mod)
    invs[i] %= mod
ans = comb_mod(C+D+2,C+1,mod,invs)-comb_mod(B+C+1,B,mod,invs)-comb_mod(A+D+1,A,mod,invs)+comb_mod(A+B,A,mod,invs)
print(ans%mod)