There are $N$ kinds of coins used in the Kingdom of Atcoder: $A_1$-yen, $A_2$-yen, $\dots$, $A_N$-yen coins. Here, $1=A_1 \lt \cdots \lt A_N$ 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 is given from Standard Input in the following format: > $N \quad X$\ > $A_1 \quad A_2 \quad \cdots \quad A_N$ #### Constraints - All values in input are integers. - $1 \leq N \leq 60$ - $1=A_1 \lt \cdots \lt A_N \leq 10^{18}$ - $A_{i+1}$ is a multiple of $A_i$ for every $1 \leq i \leq N-1$. - $1 \leq X \leq 10^{18}$

Print the answer.

***For Sample #1:*** 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 $5$. ***For Sample #2:*** It is optimal to pay with seven $7$-yen coins.

AtCoder [ABC231E]