Banquet Preparations 1

Description:

Input:

The first line of input data contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of the test cases.

Each test case's description is preceded by a blank line. Next comes a line that contains integers $$$n$$$ and $$$m$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$; $$$0 \leq m \leq 10^6$$$). The next $$$n$$$ lines describe dishes, the $$$i$$$-th of them contains a pair of integers $$$a_i$$$ and $$$b_i$$$ ($$$0 \leq a_i, b_i \le 10^6$$$) — the masses of fish and meat in the $$$i$$$-th dish.

It is guaranteed that it is possible to eat $$$m$$$ grams of food from each dish. In other words, $$$m \leq a_i+b_i$$$ for all $$$i$$$ from $$$1$$$ to $$$n$$$ inclusive.

The sum of all $$$n$$$ values over all test cases in the test does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, print on the first line the minimal balance value that can be achieved by eating exactly $$$m$$$ grams of food from each dish.

Then print $$$n$$$ lines that describe a way to do this: the $$$i$$$-th line should contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$0 \leq x_i \leq a_i$$$; $$$0 \leq y_i \leq b_i$$$; $$$x_i+y_i=m$$$), where $$$x_i$$$ is how many grams of fish taster should eat from the $$$i$$$-th meal and $$$y_i$$$ is how many grams of meat.

If there are several ways to achieve a minimal balance, find any of them.

Sample Input:

8

1 5
3 4

1 6
3 4

2 2
1 3
4 2

2 4
1 3
1 7

3 6
1 7
1 8
1 9

3 6
1 8
1 9
30 10

3 4
3 1
3 2
4 1

5 4
0 7
6 4
0 8
4 1
5 3

Sample Output:

0
2 3
1
3 3
0
1 1
1 1
2
1 3
0 4
3
0 6
0 6
0 6
7
1 5
1 5
6 0
0
3 1
3 1
3 1
0
0 4
2 2
0 4
3 1
1 3