def mul(n,m):  # compute n*m; n and m are nonnegative integers
    a = n
    b = m
    c = 0
    # invariant ab+c = nm
    while a != 0:
        if a&1 == 1:
            a = a - 1
            c = c + b
            # (a-1)b + (c+b) = ab -b + c + b = ab+c = nm
        a = a>>1
        b = b<<1
        # (a/2)2b+c = ab+c = nm
    return c