Almost Fault-Tolerant Database

Description:

Input:

The first line contains integers $$$n$$$ and $$$m$$$ ($$$2 \le n$$$; $$$1 \le m$$$; $$$n \cdot m \le 250\,000$$$) — the number of copies and the size of the array.

Each of the following $$$n$$$ lines describes one of the currently stored copies in the database, it consists of $$$m$$$ integers $$$s_{i, 1}, s_{i, 2}, \dots, s_{i, m}$$$ ($$$1 \le s_{i, j} \le 10^9$$$).

Output:

If there is an array consistent with all given copies, print "Yes" and then the array itself. The array must have length $$$m$$$ and contain integers between $$$1$$$ and $$$10^9$$$ only.

Otherwise, print "No".

If there are multiple possible arrays, print any of them.

Sample Input:

3 4
1 10 10 100
1 1 1 100
10 100 1 100

Sample Output:

Yes
1 10 1 100

Sample Input:

10 7
1 1 1 1 1 1 1
1 1 1 1 1 1 2
1 1 1 1 1 2 2
1 1 1 1 2 2 1
1 1 1 2 2 1 1
1 1 2 2 1 1 1
1 2 2 1 1 1 1
2 2 1 1 1 1 1
2 1 1 1 1 1 1
1 1 1 1 1 1 1

Sample Output:

Yes
1 1 1 1 1 1 1

Sample Input:

2 5
2 2 1 1 1
1 1 2 2 2

Sample Output:

No

Note:

In the first example, the array $$$[1, 10, 1, 100]$$$ differs from first and second copies in just one position, and from the third copy in two positions.

In the second example, array $$$[1, 1, 1, 1, 1, 1, 1]$$$ is the same as the first copy and differs from all other copies in at most two positions.

In the third example, there is no array differing in at most two positions from every database's copy.