First Pair with Given Sum

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Consider pairs 1<=i<j<=n in lexicographic order (i increasing, then j increasing). Print the first pair whose sum is k, or -1 if absent. An equal-index pair is invalid.

Input

One line: $n,k$; $1\le n\le1000$, $2\le k\le2n$.

Output

Print i j separated by a space, or -1.

Subtasks

• Subtask 1 (20%): $1\le n\le 15$; $2\le k\le2n$.

• Subtask 2 (30%): $1\le n\le 100$; $2\le k\le2n$.

• Subtask 3 (50%): $1\le n\le 1000$; $2\le k\le2n$.

Examples

Example 1

Input:

5 6

Output:

1 5

Explanation:

The first pair in lexicographic order meeting i<j and i+j=k is printed; otherwise -1. Result: 1 5.

Example 2

Input:

3 2

Output:

-1

Explanation:

The first pair in lexicographic order meeting i<j and i+j=k is printed; otherwise -1. Result: -1.

Example 3

Input:

1 2

Output:

-1

Explanation:

The first pair in lexicographic order meeting i<j and i+j=k is printed; otherwise -1. Result: -1.