MIT Individual Contest 2008

You are given n binary strings s₁ ... s_n, each of the same length m. Along with each s_i you are given a bit b_i. You are also given some nonnegative integer k and want to know whether there exists a subset S of {0, 1 ... m-1} of size at most k such that for each i = 1, 2 ... n, the bit b_i is the XOR of the bits of s_i at the indices in S. The s_i are 0-indexed strings. Recall that the XOR of a set of bits is 1 if the number of bits equal to 1 is odd, else the XOR is 0 (in particular, the XOR of an empty set of bits is 0). For example, if s₁ = 1010 and S = {0, 3}, then b₁ would be 1 (the first bit of s₁) XOR'd with 0 (the last bit of s₁), which is 1. Given n, k, and the strings s₁ ... s_n and their corresponding b_i, find a set S of size at most k which produces the given b_i. You should also detect when no such S exists.

Input

The first line contains n and k, space-separated (1 ≤ n ≤ 64, 0 ≤ k ≤ 10). n lines then follow, where the ith line contains s_i, followed by a space, then b_i. In a given test case all strings s_i are of the same length m (1 ≤ m ≤ 50). k will not be bigger than m.

Output

If no set S of size at most k exists producing the given b_i, output -1 followed by a newline. Otherwise, on the first line output the size of a possible S. If the size of that S is not 0, on the second line, output a space-separated list of the indices in S, followed by a newline. If there exist multiple valid S to be output, you can output any one of your choosing.

Example

Input:
3 1
111 1
001 0
011 1

Output:
1
1