题干：

An army of n droids is lined up in one row. Each droid is described by m integers a1, a2, ..., am, where ai 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?

Input

The first line contains three integers n, m, k (1 ≤ n ≤ 105, 1 ≤ m ≤ 5, 0 ≤ k ≤ 109) — 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 a1, a2, ..., am (0 ≤ ai ≤ 108), where ai is the number of details of the i-th type for the respective robot.

Output

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.

Examples

Input

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

Output

2 2

Input

3 2 4
1 2
1 3
2 2

Output

1 3

Note

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.

题目大意：

有 n 个机器人站成一排。每个机器人可以表示成 m 个整数 a1, a2, ..., am，其中 ai 是机器人的第 i 项特征值。 R2-D2 想要摧毁尽量多的连续的机器人。 他有 m 种武器， 第 i 种武器可以将所有机器人第 i 项特征值减少1。 (如果该机器人的特征值已经为0，则什么都不发生).

如果一个机器人所有特征值都为0，则认为该机器人被摧毁。R2-D2 可以用 k 次武器。问 R2-D2 最多可以摧毁多少连续的机器人？

Input

第一行包含三个整数 n, m, k (1 ≤ n ≤ 105, 1 ≤ m ≤ 5, 0 ≤ k ≤ 109) — 分别表示机器人数，特征值数和可以动用武器的次数。

之后 n 行每行描述一个机器人。每行包含 m 个整数 a1, a2, ..., am (0 ≤ ai ≤ 108)，其中 ai是这个机器人的第 i 项特征值。

Output

输出 m 个用空格分开的数，其中第 i 个数表示第 i 种武器使用的次数。

如果有多种方案，输出任意一种。

可以使用少于 k 次射击。

解题报告：

先二分，然后check的时候滑动窗口，刚开始是想拿个multiset维护窗口内元素，来寻找最大值，复杂度两个log，T了，无奈，换成ST表，复杂度降到O(nmlogn)，这题也可以直接尺取，复杂度O(nm)

AC代码：

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<queue>
#include<stack>
#include<map>
#include<vector>
#include<set>
#include<string>
#include<cmath>
#include<cstring>
#define FF first
#define SS second
#define ll long long
#define pb push_back
#define pm make_pair
using namespace std;
typedef pair<int,int> PII;
const int MAX = 2e5 + 5;
ll n,m,k;
int a[MAX][6];
int ans[6],tmp[6];
int dp[6][MAX][24],qq[MAX];
void init() {for(int k = 1; k<=m; k++) {for(int i = 1; i<=n; i++) dp[k][i][0] = a[i][k];for(int j = 1; (1<<j) <= n; j++) {for(int i = 1; i+(1<<j)-1 <= n; i++) {dp[k][i][j] = max(dp[k][i][j-1] , dp[k][i + (1<<(j-1))][j-1]);}}}for(int i = 1; i<=n; i++) {int k = 0;while(1<<(k+1) <= i) k++;qq[i] = k;}
}
int cal(int l,int r,int kk) {int k = qq[r-l+1];return max(dp[kk][l][k],dp[kk][r- (1<<k) + 1][k]);
}
bool ok(int len) {if(len == 0) return 1;ll tt=0;for(int i = 1; i+len-1<=n; i++) {tt=0;for(int j = 1; j<=m; j++) tmp[j] = cal(i,i+len-1,j),tt += tmp[j];if(tt <= k) return 1;} return 0;
}
int main()
{cin>>n>>m>>k;for(int i = 1; i<=n; i++) {for(int j = 1; j<=m; j++) {scanf("%d",&a[i][j]);}}init();int l = 0,r = n,mid,ans[6];while(l<=r) {mid = l+r>>1;if(ok(mid)) {for(int i = 1; i<=m; i++) ans[i] = tmp[i];l = mid+1;}else r = mid-1;}for(int i = 1; i<=m; i++) printf("%d ",ans[i]);return 0 ;
}
/*
1 1 0
0
*/