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.

Input

Input is given from Standard Input in the following format:
N X
$A_1 \ldots A_N$

Output

Print the answer.

Constraints

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

Sample Input 1

3 87
1 10 100

Sample Output 1

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.

Sample Input 2

2 49
1 7

Sample Output 2

7

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

Sample Input 3

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

Sample Output 3

233

见题面 Input 部分

见题面 Output 部分