Score : $500$ points

Problem Statement

There are $N$ kinds of coins used in the Kingdom of Atcoder: $A_1$-yen, $A_2$-yen, $\ldots$, $A_N$-yen coins. Here, $1=A_1 < \ldots < A_N$ holds, and $A_{i+1}$ is a multiple of $A_i$ for every $1\leq i \leq N-1$.

When paying for a product worth $X$ yen using just these coins, what is the minimum total number of coins used in payment and returned as change?

Accurately, when $Y$ is an integer at least $X$, find the minimum sum of the number of coins needed to represent exactly $Y$ yen and the number of coins needed to represent exactly $Y-X$ yen.

Constraints

• All values in input are integers.
• $1 \leq N \leq 60$
• $1=A_1 < \ldots
• $A_{i+1}$ is a multiple of $A_i$ for every $1\leq i \leq N-1$.
• $1\leq X \leq 10^{18}$

Input

Input is given from Standard Input in the following format:

$N$ $X$

$A_1$ $\ldots$ $A_N$

Output

Print the answer.

3 87
1 10 100

5

If we pay with one $100$-yen coin and receive one $10$-yen coin and three $1$-yen coins as the change, the total number of coins will be $5$.

2 49
1 7

7

It is optimal to pay with seven $7$-yen coins.

10 123456789012345678
1 100 10000 1000000 100000000 10000000000 1000000000000 100000000000000 10000000000000000 1000000000000000000

233