Mutiples on a circle

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

Tom has a necklace with n jewels. There is a number on each jewel. Now Tom wants to selesct a wonderful chain from the necklace. A chain will be regarded wonderful if the wonderful value of the chain is a multiple of a key number K. Tom gets the wonderful value using this way:He writes down the number on the chain in clockwise order and concatenate them together. In this way, he gets a decimal number which is defined as the wonderful value.

For example, consider a necklace with 5 jewels and corresponding numbers on the jewels are 9 6 4 2 8 (9 and 8 are in neighborhood). Assume we take K = 7, then we can find that only five chains can be multiples of K. They are 42, 28, 896, 42896 and 89642.

Now Tom wants to know that how many ways he can follow to select a wonderful chain from his necklace.


The input contains several test cases, terminated by EOF.

Each case begins with two integers n (1 ≤ n ≤ 50000), K (1 ≤ K ≤ 200), the length of the necklace and the key number.

The second line consists of n integer numbers, the ith number ai (1 ≤ ai ≤ 10000)indicating the number on the ith jewel. It’s given in clockwise order.


For each test case, print a number indicating how many ways Tom can follow to select a wonderful chain.

Sample Input

5 7
9 6 4 2 8

Sample Output