PARITY - Parity

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You are given n binary strings s1,...,sn, each of the same length m. Along with each si you are given a bit bi. 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 bi is the XOR of the bits of si at the indices in S. The si 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,...,sn and their corresponding bi, find a set S of size at most k which produces the given bi. 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 si, followed by a space, then bi. In a given test case all strings si 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 bi, 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

hide comments
Scape: 2016-07-30 23:30:36

Thanks guys!

Francky: 2016-07-20 14:29:27

Issue fixed, and rejudge in progress ; thanks @admins.
(Edit) => Done.

Last edit: 2016-07-21 17:59:49
Scape: 2016-07-18 01:11:08

Please fix Internal Error and rejudge all submissions. Thanks!

=(Francky)=> Mail send to admins ; please be patient.

Last edit: 2016-07-18 13:33:24
One Two Three: 2015-06-22 15:45:31

I got Internal Error submitting the solution, please fix it!

Marcel Stockli: 2012-04-12 21:24:23

somebody has problems with the case 33? I always got WA in that case.


Added by:Minilek
Date:2008-12-22
Time limit:5s-30s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:MIT Individual Contest 2008