The Travelling Salesman spends a lot of time travelling so he tends to get bored. To pass time, he likes to perform operations on numbers. One such operation is to take a positive integer x and reduce it to the number of bits set to 1 in the binary representation of x. For example for number 13 it's true that 13 in decimal = 1101 in binary, so it has 3 bits set and 13 will be reduced to 3 in one operation.

He calls a number special if the minimum number of operations to reduce it to 1 is k.

He wants to find out how many special numbers exist which are not greater than n. Please help the Travelling Salesman, as he is about to reach his destination!

Since the answer can be large, output it modulo 10^9 + 7.

Input Format

First line contains a single integer n in binary (1<=n<=2^1000)

Second line contains k where 0<=k<=1000.

Output Format

Output a single integer — the number of special numbers not greater than n, modulo 10^9 + 7.