public class Choose { 
    /* Computes 'n choose k' using its definition */
    static long recChoose(int n, int k) {
        return (k==0 || k==n) ? 1 : recChoose(n-1, k-1) + recChoose(n-1, k);
    }

    /////////////////////////////////////////////////////////////////////////////
    static long[][] dpTable;

    /*
     * Computes 'n choose k' using bottom-up dynamic programming.
     * Table-filling is row-by-row.
     */
    static long dpChooseRow(int n, int k) {
        for (int i = 0; i <= n; i++)
            for (int j = 0; j <= Math.min(i, k); j++)
                dpTable[i][j] = (j==0 || j==i) ? 1 : dpTable[i-1][j] + dpTable[i-1][j-1];
        return dpTable[n][k];
    }

    /*
     * Computes 'n choose k' using bottom-up dynamic programming.
     * Table-filling is column-by-column.
     */
    static long dpChooseColumn(int n, int k) {
        for (int j = 0; j <= k; j++)
            for (int i = j; i <= n; i++)
                dpTable[i][j] = (j==0 || j==i) ? 1 : dpTable[i-1][j] + dpTable[i-1][j-1];
        return dpTable[n][k];
    }

    static long[] array;
    /*
     * Computes 'n choose k' using bottom-up dynamic programming.
     * Table-filling is row-by-row, but we save space by using only 1D-array.
     */
    static long dpChooseSpace(int n, int k) {
        for (int i = 0; i <= n; i++)
            for (int j = Math.min(i, k); j >= 0; j--)
                array[j] = (j==0 || j==i) ? 1 : array[j-1] + array[j];
        return array[k];
    }

    /////////////////////////////////////////////////////////////////////////////
    static long[][] mzTable;
    static final long UNKNOWN = 0;

    /*
     * Computes 'n choose k' using memoization (a top-down approach).
     */
    static long mzChoose(int n, int k) {
        if (mzTable[n][k] == UNKNOWN) {
            if (k == 0 || k == n)
                mzTable[n][k] = 1;
            else
                mzTable[n][k] = mzChoose(n-1,k) + mzChoose(n-1,k-1);
        }
        return mzTable[n][k];
    }

    /////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) { 
        int n = Integer.parseInt(args[0]);
        int k = Integer.parseInt(args[1]);

        if (n < 0 || k < 0 || k > n) {
            System.err.println("invalid arguments");
            System.exit(1);
        }

        long value;
        double time;

        Stopwatch sw1 = new Stopwatch();
        value = recChoose(n, k);
        time = sw1.elapsedTime();
        System.out.printf("%nrecChoose(%d, %d) = %d%n", n, k, value);
        System.out.printf("time spent: %.2f%n", time);

        mzTable = new long[n+1][k+1];
        Stopwatch sw2 = new Stopwatch();
        value = mzChoose(n, k);
        time = sw2.elapsedTime();
        System.out.printf("%nmzChoose(%d, %d) = %d%n", n, k, value);
        System.out.printf("time spent: %.2f%n", time);

        dpTable = new long[n+1][k+1];
        Stopwatch sw3 = new Stopwatch();
        value = dpChooseRow(n, k);
        time = sw3.elapsedTime();
        System.out.printf("%ndpChooseRow(%d, %d) = %d%n", n, k, value);
        System.out.printf("time spent: %.2f%n", time);

        dpTable = new long[n+1][k+1];
        Stopwatch sw4 = new Stopwatch();
        value = dpChooseColumn(n, k);
        time = sw4.elapsedTime();
        System.out.printf("%ndpChooseColumn(%d, %d) = %d%n", n, k, value);
        System.out.printf("time spent: %.2f%n", time);

        array = new long[k+1];
        Stopwatch sw5 = new Stopwatch();
        value = dpChooseSpace(n, k);
        time = sw5.elapsedTime();
        System.out.printf("%ndpChooseSpace(%d, %d) = %d%n", n, k, value);
        System.out.printf("time spent: %.2f%n%n", time);

    }
}