def build(num, probs):
    probs = sorted(probs)
    res = []
    if num == 1:
        index = probs[0][1]
        res.append(('', index))
    if num >= 2:
        first = probs[0]
        second = probs[1]
        probs[1] = (first[0] + second[0], second[1])
        for i in build(num - 1, probs[1:]):
            res.append(i)
        for i in res:
            if i[1] == probs[1][1]:
                ans = i
                res.append((ans[0] + '0', first[1]))
                res.append((ans[0] + '1', second[1]))
                res.remove(ans)
                break
    return res