Problem:
Score : 600 points

Problem Statement

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).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

# coding: utf-8
from math import factorial
mod = 10**9 + 7
r1, c1, r2, c2 = map(int, input().split())
def comb(r, c):
    return factorial(r+c) // (factorial(r) * factorial(c))
if r2 - r1 < c2 - c1:
    l = [comb(r1, c1)]
    ans = l[0]
    for r in range(r1+1, r2+1):
        l.append((l[-1] * (r+c1) // (r)) % mod)
    for c in range(c1+1, c2+1):
        l.append((l[-1] * (r2+c) // c) % mod)
    cnt = 1
    for i in range(r2-r1+1):
        ans += l[i] * cnt
        ans %= mod
        cnt += 1
    c_cnt = 1
    for i in range(r2 - r1, c2 - c1 + r2 - r1+1):
        if c_cnt > (c2 - c1) - (r2 - r1):
            cnt -= 1
        else:
            cnt += 1
        ans += l[i] * cnt
        ans %= mod
else:
    # rのがでかい
    t = 0
    l = [comb(r1, c1)%mod]
    for c in range(c1+1, c2+1):
        l.append((l[-1] * (r1+c) // c) % mod)
    for r in range(r1+1, r2+1):
        l.append((l[-1] * (r+c2) // r) % mod)
    ans = 0
    cnt = 1
    for i in range(c2-c1):
        # print("cnt", cnt)
        ans += l[i] * cnt
        ans %= mod
        cnt += 1
        t += 1
    # print("ans", ans)
    # print("cnt", cnt)
    # print("t", t)
    for i in range(t, len(l)-(c2-c1)-1):
        ans += l[i] * cnt
        ans %= mod
        t += 1
    # print("t", t)
    # print("ans", ans)
    # print("cnt", cnt)
    for i in range(t, len(l)):
        ans += l[i] * cnt
        ans %= mod
        cnt -= 1
        t += 1
print(ans % mod)
# print((r2 - r1) - (c2 - c1))
# print(t)
# print(len(l))