First Pair of Squares: Exit Both Loops

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given n,T, enumerate pairs 1<=i<j<=n lexicographically (i increasing, then j increasing). Print the first pair satisfying ii+jj=T, or -1 -1 if none. An inner-loop break alone does not stop the outer loop, so carry the found flag to it.

Input

One line contains n,T; 2<=n<=100 and 2<=T<=20000.

Output

Print i and j separated by one space, or -1 -1.

Subtasks

• Subtask 1 (20%): $2\le n\le 10$; $2\le T\le20000$.

• Subtask 2 (30%): $2\le n\le 40$; $2\le T\le20000$.

• Subtask 3 (50%): $2\le n\le 100$; $2\le T\le20000$.

Examples

Example 1

Input:

5 25

Output:

3 4

Explanation:

Loop i then j in ascending order; report the first qualifying pair. Exact input: "5 25\n"; exact output: "3 4\n".

Example 2

Input:

3 2

Output:

-1 -1

Explanation:

Loop i then j in ascending order; report the first qualifying pair. Exact input: "3 2\n"; exact output: "-1 -1\n".

Example 3

Input:

5 100

Output:

-1 -1

Explanation:

Loop i then j in ascending order; report the first qualifying pair. Exact input: "5 100\n"; exact output: "-1 -1\n".

Example 4

Input:

5 5

Output:

1 2

Explanation:

Loop i then j in ascending order; report the first qualifying pair. Exact input: "5 5\n"; exact output: "1 2\n".