You are given a square grid of size N, with rows numbered from 0 to N - 1 starting from the top and columns numbered from 0 to N - 1 starting from the left.
A cell (u, v) refers to the cell that is on the uth row and the vth column. Each cell contains an integer - 0 or 1. You can pick any cell and flip the number in all the cells (including the picked cell) within the Manhattan distance D from the picked cell. A flip here means changing the number from 0 to 1 and vice-versa. The manhattan distance from the cell (u, v) to the cell (x, y) is equal to where is the absolute value of i.
Your mission is to change all values in the grid to zero without using more than N×N flips.
Input Format
The first line of the input contains two integers N and D separated by a single space.
Each line in the next N lines contains N integers separated by a single space which are either 0 or 1. the ith number on the jth line is the number on the cell (i - 1, j - 1) of the grid.
Constraints
1 ≤ N ≤ 20
0 ≤ D ≤ 40
Output Format
If there is no solution, your output should contain exactly a single string "Impossible" (without quotes). If a solution exists, print out the string "Possible" (without quotes) in the first line of your output. In the second line, print out an integer M which represent the number of operations that you need. Each line in the next M lines should contain a pair of integers separated by a single space representing the cell that you picked for the corresponding operation. Note that if there is more than one solution you can pick any one of them.
Sample Input:#00
3 1
0 1 0
1 1 1
0 1 0
Sample Output:#00
Possible
1
1 1
Sample Input:#01
3 2
1 0 1
1 1 0
0 0 0
Sample Output:#01
Impossible
Explanation
In the first testcase, we can perform the first operation in the center cell, this will flip all the elements to 0 within 1 manhattan distance.
In the second testcase, we cannot make it an all 0 matrix under 9 moves. Hence, Impossible.