Problem Description

E869120 went to a store called AtCoder Rotating Sushi.
There are $ N $ sushi at this store, each labeled with numbers $1,\ 2,\ 3,\ \cdots,\ N$. Sushi $ i $ can only be taken at times $ a_i+kT $ seconds after he arrives ($ k $ is a non-negative integer).

He wants to eat the sushi in the order of sushi $ 1 $ → sushi $ 2 $ → … → sushi $ N $. However, he is greedy and will eat a sushi as soon as he takes it. Determine the minimum number of seconds from his arrival until he finishes eating all $ N $ sushi. Time to take or eat sushi can be ignored, and he can take sushi that arrives at $ 0 $ seconds after his arrival.

Input Format

Input is given from the standard input in the following format:

$ N $ $ T $ $ a_1 $ $ a_2 $ $ a_3 $ ... $ a_N $

Output Format

Output the minimum number of seconds required to finish eating all the sushi in the specified order.

Sample Input and Output

Sample Input #1

1 6
4

Sample Output #1

4

Sample Input #2

3 10
3 7 2

Sample Output #2

12

Sample Input #3

6 15
8 6 9 1 2 0

Sample Output #3

45

Notes/Hints

Constraints

• $ N $ is an integer between $ 1 $ and $ 100 $ inclusive.
• $ T $ is an integer between $ 1 $ and $ 100 $ inclusive.
• $ a_i $ is an integer between $ 0 $ and $ T-1 $ inclusive $(1\ \leq\ i\ \leq\ N)$.
• For $1\ \leq\ i\ <\ j\ \leq\ N$, $a_i\ \neq\ a_j$.

Subtasks

Subtask $ 1 $ \[$ 100 $ points\]

• $N\ =\ 1$.

Subtask $ 2 $ \[$ 100 $ points\]

• No additional constraints.

Sample Explanation 1

In this case, sushi $ 1 $ can be taken at $4,\ 10,\ 16,\ 22,\ 28,\ \cdots$ seconds after arrival. The earliest is at $ 4 $ seconds.

Sample Explanation 2

The shortest time to take sushi $1,\ 2,\ 3$ is at $3,\ 7,\ 12$ seconds respectively.

见题面 Input 部分

见题面 Output 部分