#P1389A. LCM Problem

    ID: 1434 远端评测题 2000ms 256MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>constructive algorithmsgreedymathnumber theory*800

LCM Problem

Description

Let LCM(x,y)LCM(x, y) be the minimum positive integer that is divisible by both xx and yy. For example, LCM(13,37)=481LCM(13, 37) = 481, LCM(9,6)=18LCM(9, 6) = 18.

You are given two integers ll and rr. Find two integers xx and yy such that lx<yrl \le x < y \le r and lLCM(x,y)rl \le LCM(x, y) \le r.

The first line contains one integer tt (1t100001 \le t \le 10000) — the number of test cases.

Each test case is represented by one line containing two integers ll and rr (1l<r1091 \le l < r \le 10^9).

For each test case, print two integers:

  • if it is impossible to find integers xx and yy meeting the constraints in the statement, print two integers equal to 1-1;
  • otherwise, print the values of xx and yy (if there are multiple valid answers, you may print any of them).

Input

The first line contains one integer tt (1t100001 \le t \le 10000) — the number of test cases.

Each test case is represented by one line containing two integers ll and rr (1l<r1091 \le l < r \le 10^9).

Output

For each test case, print two integers:

  • if it is impossible to find integers xx and yy meeting the constraints in the statement, print two integers equal to 1-1;
  • otherwise, print the values of xx and yy (if there are multiple valid answers, you may print any of them).

Samples

样例输入 1

4
1 1337
13 69
2 4
88 89

样例输出 1

6 7
14 21
2 4
-1 -1