如何找到乘以固定乘积的所有可能的向量组合？

def find_vector_combinations(product, dimension):
    result = []
    vector = [1] * dimension  # 初始化向量为全1

    def generate_combinations(curr_dimension, curr_product):
        nonlocal vector, result

        if curr_dimension == dimension:
            if curr_product == product:
                result.append(vector.copy())
            return

        for i in range(1, product + 1):
            vector[curr_dimension] = i
            generate_combinations(curr_dimension + 1, curr_product * i)

    generate_combinations(0, 1)
    return result

# 示例调用
product = 6
dimension = 3
combinations = find_vector_combinations(product, dimension)
for combination in combinations:
    print(combination)

[1, 1, 6]
[1, 2, 3]
[1, 3, 2]
[1, 6, 1]
[2, 1, 3]
[2, 3, 1]
[3, 1, 2]
[3, 2, 1]
[6, 1, 1]