Card Game

문제

Vilius and Adomas play a simple card game. They have a deck of $NN$ cards. Every card contains a number. Each player draws two random cards from the deck, adds the two numbers on the cards, and the player with the larger sum wins.

Vilius chose a number $CC$ and wants to win by exactly $CC$ points. In other words, he wants the sum of his cards minus the sum of Adomas's cards to be exactly $CC$. How many ways there are for Vilius and Adomas to draw their cards so that Vilius wins by exactly $CC$ points?

The same number can be written on multiple cards. Then the case when a player draws one or another of them are considered distinct. The order of the two cards in a player's hand, however, does not matter. For example, if two cards contain the number $11$ and three cards contain the number $22$, there would be six ways for Adomas to draw cards with numbers $11$ and $22$.

입력

The first line contains two integers $NN$ and $CC$ ($4\le N\le 15004\; \backslash le\; N\; \backslash le\; 1\backslash ,500$, $0\le C\le {10}^{9}0\; \backslash le\; C\; \backslash le\; 10^9$), the number of cards in the deck and the desired score difference, respectively. The second line contains $NN$ integers $A_1,A_2,\dots ,A_{N}A\_1,\; A\_2,\; \backslash ldots,\; A\_N$ ($0\le A_i\le {10}^{9}0\; \backslash le\; A\_i\; \backslash le\; 10^9$), the numbers on the cards.

출력

Output a single integer: the number of ways the players can draw cards so that Vilius wins by exactly $CC$ points.