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Problem 1420 Twinkling lights II

## Problem Description

Do you remember the problem "Twinkling lights" in FJNUPC 2005? It's a funny problem, Now let's change some conditions to make it a new problem -_- .
There is a line consisting of n lights numbered as 1, 2, …,n. At time 0, some lights are on and the others are off. Light i controls some lights(possibly includes itself). At time t+1, light i will change these lights' status if light i is on at time t. So light j would alter its status(from on to off or from off to on), only if light j is altered by odd times. Please work out how many lights are on at time m.

## Input

The first line of the input is an integer T denoting the number of test cases. The first line of each test case consists of two integers separated by one space, where the first integer n (0 < n <= 100) denotes the number of lights and the second integer is m (0 < m <= 1,000,000,000). The second line is a binary string of length n, representing the status of each light at time 0 ("1" denoting the light is on and "0" denoting the light is off). Then follows n lines, the ith line starts with an interger si,which is the number of lights controlled by light i. Then follows si intergers, denoting the lights controlled by light i.

## Output

For each test case, output an interger representing the lights that are on at time m.

## Sample Input

2 3 2 010 3 1 3 2 1 3 1 1 2 2 11 2 1 2 0

2 0

## Hint

The first test case: 010->011->110 The second test case: 11->00->00

## Source

FZU ICPC Preliminary Round 2006

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