Problem

Aizu decided to play a game using a prime number $ P $, a set of natural numbers $ G $, and a natural number $ A $.

First, Aizu writes $ 1 $ on the paper at hand. After that, perform the following series of operations any number of times.

• Select one element from $ G $. Let this be $ g $.
• Write a new product of the number written on the paper at hand and $ g $ on the paper.
• Erase the number originally written on the paper.

If $ A $ is equal to the number written on the paper at hand divided by $ P $, Aizu wins, otherwise he loses. Determine if Aizu can win when $ P $, $ G $, and $ A $ are given.

Constraints

The input satisfies the following conditions.

• All inputs are integers.
• $2 \ le P \ le 2 ^ {31} -1$
• $1 \ le T, | G | \ le 10 ^ 5$
• $1 \ le G_i, A \ le P-1$
• $G_i \ ne G_j,$ if $i \ ne j$
• The sum of $ | G | $ in all test cases does not exceed $ 10 ^ 5 $.

Input

The input is given in the following format.

$ P $ $ T $
$ Test_1 $
$\$
$ Test_ {T} $

The input consists of multiple test cases. First, the $ 1 $ line is given the prime number $ P $ and the number of test cases $ T $. $ P $ is common to all test cases. Each test case is given in the following $ T $ line.

Each test case is given as follows.

$ | G | $ $ G_1 $ $\$ $ G_ {| G |} $ $ A $

In each test case, the number of elements of $ G $, each element of $ G $, and $ A $ are given in order, separated by a space.

Output

For each test case, if Aizu can win, $ 1 $ will be output on one line, otherwise $ 0 $ will be output on one line.

Examples

Input

7 3
1 1 2
1 2 1
3 1 2 4 5

Output

0
1
0

Input

1000000007 8
3 2 9 7 5
3 2 9 5 1000001
3 39 1002 65537 12
2 1000000006 518012930 793649232
10 459268180 313723762 835892239 612038995 90424474 366392946 38051435 854115735 5132833 320534710 421820264
1 1 1
1 1 1000000006
1 1000000006 1

Output

0
1
1
1
0
1
0
1

见题面

见题面