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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.BufferedReader
import java.io.InputStream
import java.io.InputStreamReader
import java.util.*

val mod = (1e9 + 7).toLong()
val fact = Array((2e6 + 2).toInt()) { 1L }
fun main(args: Array<String>) {
    val sc = FastScanner(System.`in`)

    val r1 = sc.nextInt()
    val c1 = sc.nextInt()
    val r2 = sc.nextInt()
    val c2 = sc.nextInt()

    for (i in 2 until fact.size) fact[i] = (i * fact[i - 1]) % mod

    var ans = C(r1, r1 + c1)
    for(r in r1 + 1..r2) ans = (ans + C(r, r +c2)) % mod
    for(c in c1 + 1..c2) ans = (ans + C(c, r2 +c)) % mod

    println(ans)
}

fun C(k: Int, n: Int): Long {
    var res = (fact[n] * inv(fact[n - k])) % mod
    res = (res * inv(fact[k])) % mod
    return res
}

fun inv(x: Long): Long = pow(x, mod - 2)
fun pow(a: Long, x: Long): Long {
    var a = a
    var x = x
    var res = 1L
    while (x > 0) {
        if (x % 2 == 1L) res = (res * a) % mod
        a = (a * a) % mod
        x /= 2
    }
    return res
}

class FastScanner(s: InputStream) {
    private var st = StringTokenizer("")
    private val br = BufferedReader(InputStreamReader(s))

    fun next(): String {
        while (!st.hasMoreTokens()) st = StringTokenizer(br.readLine())

        return st.nextToken()
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextLine() = br.readLine()
    fun nextDouble() = next().toDouble()
    fun ready() = br.ready()
}