#P1478B. Nezzar and Lucky Number

Nezzar and Lucky Number

Description

Nezzar's favorite digit among 1,,91,\ldots,9 is dd. He calls a positive integer lucky if dd occurs at least once in its decimal representation.

Given qq integers a1,a2,,aqa_1,a_2,\ldots,a_q, for each 1iq1 \le i \le q Nezzar would like to know if aia_i can be equal to a sum of several (one or more) lucky numbers.

The first line contains a single integer tt (1t91 \le t \le 9) — the number of test cases.

The first line of each test case contains two integers qq and dd (1q1041 \le q \le 10^4, 1d91 \le d \le 9).

The second line of each test case contains qq integers a1,a2,,aqa_1,a_2,\ldots,a_q (1ai1091 \le a_i \le 10^9).

For each integer in each test case, print "YES" in a single line if aia_i can be equal to a sum of lucky numbers. Otherwise, print "NO".

You can print letters in any case (upper or lower).

Input

The first line contains a single integer tt (1t91 \le t \le 9) — the number of test cases.

The first line of each test case contains two integers qq and dd (1q1041 \le q \le 10^4, 1d91 \le d \le 9).

The second line of each test case contains qq integers a1,a2,,aqa_1,a_2,\ldots,a_q (1ai1091 \le a_i \le 10^9).

Output

For each integer in each test case, print "YES" in a single line if aia_i can be equal to a sum of lucky numbers. Otherwise, print "NO".

You can print letters in any case (upper or lower).

Samples

样例输入 1

2
3 7
24 25 27
10 7
51 52 53 54 55 56 57 58 59 60

样例输出 1

YES
NO
YES
YES
YES
NO
YES
YES
YES
YES
YES
YES
NO

Note

In the first test case, 24=17+724 = 17 + 7, 2727 itself is a lucky number, 2525 cannot be equal to a sum of lucky numbers.