You have $$$n$$$ rectangles, the $$$i$$$-th of which has a width of $$$a_i$$$ and a height of $$$b_i$$$.

You can perform the following operation an unlimited number of times: choose a rectangle and a cell in it, and then color it.

Each time you completely color any row or column, you earn $$$1$$$ point. Your task is to score at least $$$k$$$ points with as few operations as possible.

Suppose you have a rectangle with a width of $$$6$$$ and a height of $$$3$$$. You can score $$$4$$$ points by coloring all the cells in any $$$4$$$ columns, thus performing $$$12$$$ operations.

Input format:
The first line contains an integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The following are the descriptions of the test cases.

The first line of each test case description contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 1000, 1 \le k \le 100$$$) — the number of rectangles in the case and the required number of points.

The next $$$n$$$ lines contain the descriptions of the rectangles. The $$$i$$$-th line contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le 100$$$) — the width and height of the $$$i$$$-th rectangle.

It is guaranteed that the sum of the values of $$$n$$$ across all test cases does not exceed $$$1000$$$.
Output format:
For each test case, output a single integer — the minimum number of operations required to score at least $$$k$$$ points. If it is impossible to score at least $$$k$$$ points, output -1.
Example Input 0:
7
1 4
6 3
1 5
4 4
5 10
1 1
1 1
1 1
1 1
1 1
2 100
1 2
5 6
3 11
2 2
3 3
4 4
3 25
9 2
4 3
8 10
4 18
5 4
8 5
8 3
6 2

Example Output 0:
12
14
5
-1
17
80
35



Example input:
7
1 4
6 3
1 5
4 4
5 10
1 1
1 1
1 1
1 1
1 1
2 100
1 2
5 6
3 11
2 2
3 3
4 4
3 25
9 2
4 3
8 10
4 18
5 4
8 5
8 3
6 2


Example output:
12
14
5
-1
17
80
35