题目背景

老唐最近迷上了飞盘，约翰想和他一起玩，于是打算从他家的N头奶牛中选出一支队伍。
每只奶牛的能力为整数，第i头奶牛的能力为R i 。飞盘队的队员数量不能少于 1、大于N。一
支队伍的总能力就是所有队员能力的总和。
约翰比较迷信，他的幸运数字是F，所以他要求队伍的总能力必须是F的倍数。请帮他
算一下，符合这个要求的队伍组合有多少？由于这个数字很大，只要输出答案除以$10^8$ 的余
数就可以了。

输入格式

第一行：两个用空格分开的整数：N和F，1 ≤ N ≤ 2000，1 ≤ F ≤ 1000
第二行到N + 1行：第i + 1行有一个整数R i ，表示第i头奶牛的能力，1 ≤ R i ≤ 10 5

输出格式

 第一行：单个整数，表示方案数除以$10^8$ 的余数
样例 fristeam.in fristeam.out
4 5 1 2 8 2 3 （有两种方案都是8 + 2 = 10，只是选的奶牛）

题目描述

After Farmer Don took up Frisbee, Farmer John wanted to join in the fun. He wants to form a Frisbee team from his N cows (1 <= N <= 2,000) conveniently numbered 1..N. The cows have been practicing flipping the discs around, and each cow i has a rating R_i (1 <= R_i <= 100,000) denoting her skill playing Frisbee. FJ can form a team by choosing one or more of his cows.
However, because FJ needs to be very selective when forming Frisbee teams, he has added an additional constraint. Since his favorite number is F (1 <= F <= 1,000), he will only accept a team if the sum of the ratings of each cow in the team is exactly divisible by F.
Help FJ find out how many different teams he can choose. Since this number can be very large, output the answer modulo 100,000,000.
Note: about 50% of the test data will have N <= 19. 
农夫顿因开始玩飞盘之后，约翰也打算让奶牛们享受飞盘的乐趣．他要组建一只奶牛飞盘
队．他的N(1≤N≤2000)只奶牛，每只部有一个飞盘水准指数Ri(1≤Ri≤100000)．约翰要选出1只或多于1只奶牛来参加他的飞盘队．由于约翰的幸运数字是F(1≤F≤1000)，他希望所有奶牛的飞盘水准指数之和是幸运数字的倍数．
帮约翰算算一共有多少种组队方式．

输入格式：

Line 1: Two space-separated integers: N and F
Lines 2..N+1: Line i+1 contains a single integer: R_i

输出格式：

Line 1: A single integer representing the number of teams FJ can choose, modulo 100,000,000.

输入样例#1：

4 5 
1 
2 
8 
2 

输出样例#1：

3