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 = int(1e9)+7

def fact(x):
    k = 1
    for i in range(1,x+1):
        k = (k*i)%MOD
    return k

def inverse(b):
    r = 1
    e = MOD -2
    while e:
        if e%2==1:
            r = (r*b)%MOD
        b = (b*b)%MOD
        e >>=1
    return r

def comb(i,j):
    if i==0 or j==0:
        return 0
    num=fact(i+j)
    num*=inverse(fact(i))
    num%=MOD
    num*=inverse(fact(j))
    num%=MOD
    return num

rc = list(map(int, input().split()))
ans = 0
ans += comb(rc[2]+1,rc[3]+1)
ans -= comb(rc[0],rc[3]+1)
ans -= comb(rc[2]+1,rc[1])
ans += comb(rc[0],rc[1])
ans += MOD
ans += MOD
ans %=MOD
print(ans)