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
#0<=i<r,0<=j<cで総和求めて引く
#chooseの+2でよい
mod = 10**9+7

def chs(a,b):
    a+=1;b+=1
    a+=b
    res = 1
    for i in range(a,a-b,-1):
        res *= i 
        res%=mod
    for i in range(1,b+1):
        res *= rev[i]
        #print(rev[i],pow(i,mod-2,mod))
        res %=mod 
    return res


r1,c1,r2,c2 = map(int, input().split( ))
r1 -=1;c1-=1
if c2>r2:
    r2,c2 = c2,r2
    r1,c1= c1,r1
rev = [pow(i,mod-2,mod) for i in range(c2+5)]###
ans = chs(r2,c2)-chs(r1,c2)-chs(r2,c1)+chs(r1,c1)
ans%=mod
#print(chs(r2,c2),chs(r1,c2),chs(r2,c1),chs(r1,c1))

print(ans)