import itertools
# composition devides n into all possible combinations k of ints that sum to n
# inputs: k and n are of type 'int'
# output: a set of tuples
def compositions(k, n):

    if k <= 0:
        return set()
    if k ==1:
        return set((n,))
    it = itertools.combinations(range(1,n),k-1)
    tu=set()
    s=list()
    for i in it:
        s.append(i)
    sl= sorted(s)
    for i in sl:
        nl =list()
        nl.append(i[0])
        for t in range(1,k-1):
            nl.append(i[t]-i[t-1])
        nl.append(n-i[k-2])
        tu.add(tuple(nl))
    return tu