try:
    from hashlib import blake2s
except:
    from pyblake2 import blake2s
blake = lambda x: blake2s(x).digest()

def merkelize(L):
    nodes = [b''] * len(L) + [x.to_bytes(32, 'big') if isinstance(x, int) else x for x in L]
    for i in range(len(L) - 1, 0, -1):
        nodes[i] = blake(nodes[i*2] + nodes[i*2+1])
    return nodes

def mk_branch(tree, index):
    index += len(tree) // 2
    o = [tree[index]]
    while index > 1:
        o.append(tree[index ^ 1])
        index //= 2
    return o

def verify_branch(root, index, proof, output_as_int=False):
    index += 2**len(proof)
    v = proof[0]
    for p in proof[1:]:
        if index % 2:
            v = blake(p + v)
        else:
            v = blake(v + p)
        index //= 2
    assert v == root
    return int.from_bytes(proof[0], 'big') if output_as_int else proof[0]