Problem Statement

Takahashi has N cards in his hand.
For $i = 1, 2, \ldots, N$, the i-th card has an non-negative integer A_i written on it.
First, Takahashi will freely choose a card from his hand and put it on a table.
Then, he will repeat the following operation as many times as he wants (possibly zero).

• Let X be the integer written on the last card put on the table. If his hand contains cards with the integer X or the integer $(X+1)\bmod M$ written on them, freely choose one of those cards and put it on the table. Here, $(X+1)\bmod M$ denotes the remainder when (X+1) is divided by M.

Print the smallest possible sum of the integers written on the cards that end up remaining in his hand.

Input

The input is given from Standard Input in the following format:
N M
$A_1 A_2 \ldots A_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $2 \leq M \leq 10^9$
• $0 \leq A_i \lt M$
• All values in the input are integers.

Sample Input 1

9 7
3 0 2 5 5 3 0 6 3

Sample Output 1

11

Assume that he first puts the fourth card (5 is written) on the table and then performs the following.

• Put the fifth card (5 is written) on the table.
• Put the eighth card (6 is written) on the table.
• Put the second card (0 is written) on the table.
• Put the seventh card (0 is written) on the table.

Then, the first, third, sixth, and ninth cards will end up remaining in his hand, and the sum of the integers on those cards is 3 + 2 + 3 +3 = 11.
This is the minimum possible sum of the integers written on the cards that end up remaining in his hand.

Sample Input 2

1 10
4

Sample Output 2

0

Sample Input 3

20 20
18 16 15 9 8 8 17 1 3 17 11 9 12 11 7 3 2 14 3 12

Sample Output 3

99

见题面 Input 部分

见题面 Output 部分