List

You are given a list $L$ containing all natural numbers from $1$ to $n$ in order. If you move the last $k$ numbers of this list to the front, you obtain a new list $L_1$. For example, moving the last three numbers of the list $1, 2, 3, 4, 5, 6, 7$ to the front gives $5, 6, 7, 1, 2, 3, 4$.

Given two integers $i$ and $j$ in the range $[1, n]$, you want to find the sum of the elements of $L_1$ from the $i$-th to the $j$-th position, inclusive. For the list above with $i = 2$ and $j = 6$, that sum is $6 + 7 + 1 + 2 + 3 = 19$.

Write a program that reads $n$, $k$, $i$, and $j$ from standard input, computes the sum of the elements of $L_1$ from the $i$-th to the $j$-th position, and prints the result to standard output.

The first and only line contains four integers $n$, $k$, $i$, and $j$ separated by single spaces ($2 \le n \le 10^9$, $1 \le k \le n$, $1 \le i \le j \le n$).

Print a single integer equal to the sum of the elements of $L_1$ from the $i$-th to the $j$-th position, inclusive.