{"raw_statement":[{"iden":"problem statement","content":"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.\nFirst, 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).\n\n*   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 $M$.\n\nPrint the smallest possible sum of the integers written on the cards that end up remaining in his hand."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $2 \\leq M \\leq 10^9$\n*   $0 \\leq A_i \\lt M$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"9 7\n3 0 2 5 5 3 0 6 3"},{"iden":"sample output 1","content":"11\n\nAssume that he first puts the fourth card ($5$ is written) on the table and then performs the following.\n\n*   Put the fifth card ($5$ is written) on the table.\n*   Put the eighth card ($6$ is written) on the table.\n*   Put the second card ($0$ is written) on the table.\n*   Put the seventh card ($0$ is written) on the table.\n\nThen, 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."},{"iden":"sample input 2","content":"1 10\n4"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"20 20\n18 16 15 9 8 8 17 1 3 17 11 9 12 11 7 3 2 14 3 12"},{"iden":"sample output 3","content":"99"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}