Count Pairs with Sum k

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n,k$, count pairs of integers $(i,j)$ satisfying $1\le i<j\le n$ and $i+j=k$. Each unordered pair is counted exactly once; print 0 if none exists.

Input

One line contains two integers $n,k$.

Output

Print the number of valid pairs.

Subtasks

• Subtask 1 (20%): $1\le n\le 20$; $2\le k\le 2n$.

• Subtask 2 (30%): $1\le n\le 150$; $2\le k\le 2n$.

• Subtask 3 (50%): $1\le n\le 1000$; $2\le k\le 2n$.

Examples

Example 1

Input:

4 5

Output:

2

Explanation:

For n=4, k=5, qualifying pairs are (1,4), (2,3); the answer is 2.

Example 2

Input:

1 2

Output:

0

Explanation:

For n=1, k=2, qualifying pairs are none; the answer is 0.