TopCoder SRM584: Excavations2

public class Excavations2 {
    long?[,] choose = new long?[55, 55];
    long Choose(int s, int t) {
        if (!choose[s, t].HasValue) {
            if (t == 0 || t == s)
                choose[s, t] = 1;
            else
                choose[s, t] = Choose(s - 1, t - 1) + Choose(s - 1, t);
        }
        return choose[s, t].Value;
    }

    public long count(int[] kind, int[] found, int K) {
        int N = kind.Length;
        var hist = new int[55];
        foreach (var k in kind) hist[k]++;
        var dp = new long[K + 1];
        dp[0] = 1;
        foreach (var f in found) {
            var next = new long[K + 1];
            for (int j = K - 1; j >= 0; j--) {
                for (int add = 1; add <= hist[f]; add++) {
                    if (j + add <= K) {
                        next[j + add] += dp[j] * Choose(hist[f], add);
                    }
                }
            }
            dp = next;
        }
        return dp[K];
    }
}