# given a list of categories giving the number of multi-combinations of each type,
# e.g. [1, 3, 2] would correspond to strings like 011122
# generate each permutation in order
# if two categories have the same quantity, only generates permutations in which
# the first element of the lower-numbered category comes before the first element of the higher-numbered category
def combEnum2(categories):
    n = sum(categories)
    # start with minimum permutation
    result = []
    for j,k in enumerate(categories):
        result.extend([j]*k)
    n = len(result)
    teamsUsed = list(categories)
    while True:
        print result
        x = n-2
        teamsUsed[result[x+1]] -= 1
        teamsUsed[result[x]] -= 1
        while True:
            if result[x] < result[x+1]:
                firstX = teamsUsed[result[x]] == 0
                swap = 9999
                swapIndex = -1
                for y in xrange(x+1,n):
                    if result[y] < swap and result[y] > result[x] \
                       and (not firstX or categories[result[y]] != categories[result[x]]):
                        if teamsUsed[result[y]] == 0:
                            ok = True
                            for t in xrange(result[y]):
                                if teamsUsed[t] == 0 and categories[result[y]] == categories[t]:
                                    ok = False
                        if ok:
                            swap = result[y]
                            swapIndex = y
                if swapIndex > -1:
                    teamsUsed[swap] += 1
                    result[x] = swap
                    z = 0
                    for y in xrange(x+1, n):
                        while teamsUsed[z] == categories[z]:
                            z += 1
                        result[y] = z
                        teamsUsed[z] += 1
                    break
            x-=1
            if x < 0:
                break
            teamsUsed[result[x]] -= 1
        if x < 0:
            break