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.

Constraints

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

Examples

Input:
rows = 4

Expected output:
expected = [
    [1],
    [1, 1],
    [1, 2, 1],
    [1, 3, 3, 1]
]

Input:
long long rows = 4;

Expected output:
std::vector<std::vector<long long>> expected = {
    {1},
    {1, 1},
    {1, 2, 1},
    {1, 3, 3, 1}
};

Input:
long rows = 4;

Expected output:
long[][] expected = new long[][] {
    new long[] {1},
    new long[] {1, 1},
    new long[] {1, 2, 1},
    new long[] {1, 3, 3, 1}
};

Input:
rows = 0

Expected output:
expected = []

Input:
long long rows = 0;

Expected output:
std::vector<std::vector<long long>> expected = {};

Input:
long rows = 0;

Expected output:
long[][] expected = new long[][] {};

References

This challenge is adapted for CodeUtility. Follow the statement and constraints above.

• Pascal's Triangle