R2D2 and Droid Army

一共有N个人，每个人有M个属性值，当一个人的所有属性值都小于等于0的时候，这个人就算被销毁了。 我们每次操作可以选一种属性值进行攻击，使得所有人的这个属性的值都-1. 我们最多可以进行K次操作， 问我们最多可以干掉多少个连续的人。 问这种时候的具体操作（每一种属性用了多少次操作）。

An army of $ n $ droids is lined up in one row. Each droid is described by $ m $ integers $ a_{1},a_{2},...,a_{m} $ , where $ a_{i} $ is the number of details of the $ i $ -th type in this droid's mechanism. R2-D2 wants to destroy the sequence of consecutive droids of maximum length. He has $ m $ weapons, the $ i $ -th weapon can affect all the droids in the army by destroying one detail of the $ i $ -th type (if the droid doesn't have details of this type, nothing happens to it). A droid is considered to be destroyed when all of its details are destroyed. R2-D2 can make at most $ k $ shots. How many shots from the weapon of what type should R2-D2 make to destroy the sequence of consecutive droids of maximum length?

The first line contains three integers $ n,m,k $ ( $ 1<=n<=10^{5} $ , $ 1<=m<=5 $ , $ 0<=k<=10^{9} $ ) — the number of droids, the number of detail types and the number of available shots, respectively. Next $ n $ lines follow describing the droids. Each line contains $ m $ integers $ a_{1},a_{2},...,a_{m} $ ( $ 0<=a_{i}<=10^{8} $ ), where $ a_{i} $ is the number of details of the $ i $ -th type for the respective robot.

Print $ m $ space-separated integers, where the $ i $ -th number is the number of shots from the weapon of the $ i $ -th type that the robot should make to destroy the subsequence of consecutive droids of the maximum length. If there are multiple optimal solutions, print any of them. It is not necessary to make exactly $ k $ shots, the number of shots can be less.

5 2 4
4 0
1 2
2 1
0 2
1 3

2 2

3 2 4
1 2
1 3
2 2

1 3

In the first test the second, third and fourth droids will be destroyed. In the second test the first and second droids will be destroyed.