Pascal’s Triangle

The first row is [1]. Each later row starts and ends with 1. Every interior entry is the sum of the two entries immediately above it. Return the first rows rows, beginning with the single 1.

Implement pascals_triangle(rows).

Input

rows: How many rows to generate.

Output

Return a list of rows, starting at the top; each row is a list of integers.

制約

0 ≤ rows ≤ 60. Every entry fits a signed 64-bit integer. Zero rows returns an empty list.

例

入力：
rows = 4

期待される出力：
expected = [
    [1],
    [1, 1],
    [1, 2, 1],
    [1, 3, 3, 1]
]

入力：
long long rows = 4;

期待される出力：
std::vector<std::vector<long long>> expected = {
    {1},
    {1, 1},
    {1, 2, 1},
    {1, 3, 3, 1}
};

入力：
long rows = 4;

期待される出力：
long[][] expected = new long[][] {
    new long[] {1},
    new long[] {1, 1},
    new long[] {1, 2, 1},
    new long[] {1, 3, 3, 1}
};

入力：
rows = 0

期待される出力：
expected = []

入力：
long long rows = 0;

期待される出力：
std::vector<std::vector<long long>> expected = {};

入力：
long rows = 0;

期待される出力：
long[][] expected = new long[][] {};

参考資料

この課題はCodeUtility用に調整されています。上記の説明と制約に従ってください。

• Pascal's Triangle