1. 首先提交如下代码，发现所有测试点均 RE。

n, m, k = map(int, input().split())
matrix = [[0 for _ in range(m + 1)]] + [[0] + list(map(int, input().split())) for i in range(1, n + 1)]
prefix_sum = [[0] * (m + 1) for _ in range(n + 1)]

for i in range(1, n + 1):
    for j in range(1, m + 1):
        prefix_sum[i][j] = prefix_sum[i - 1][j] + matrix[i][j]

ans = 0
for i1 in range(1, n + 1):
    for i2 in range(i1, n + 1):
        j1 = 1
        num_sum = 0
        for j2 in range(1, m + 1):
            num_sum += prefix_sum[i2][j2] - prefix_sum[i1 - 1][j2]
            while num_sum > k and j1 <= j2:
                num_sum -= prefix_sum[i2][j1] - prefix_sum[i1 - 1][j1]
                j1 += 1
            ans += j2 - j1 + 1
print(ans)

2. 于是乎，提交如下代码测试输入数据：

n, m, k = map(int, input().split())
matrix = [[0 for _ in range(m + 1)]] + [[0] + list(map(int, input().split())) for i in range(1, n + 1)]
prefix_sum = [[0] * (m + 1) for _ in range(n + 1)]

for i in range(1, n + 1):
    for j in range(1, m + 1):
        print(1)

结果显示所有测试点均为 WA，似乎并非输入数据的问题。

3. 随后，将循环体中的部分改成前缀和的计算再次提交测试：

n, m, k = map(int, input().split())
matrix = [[0 for _ in range(m + 1)]] + [[0] + list(map(int, input().split())) for i in range(1, n + 1)]
prefix_sum = [[0] * (m + 1) for _ in range(n + 1)]

for i in range(1, n + 1):
    for j in range(1, m + 1):
        prefix_sum[i][j] = prefix_sum[i - 1][j] + matrix[i][j]

结果显示全测试点 RE。但经过分析这段代码不会导致下标越界的错误？

由此，很是疑惑到底为啥 RE 的，有大佬能帮忙解答一下吗？