Codeforces 514D R2D2 and Droid Army

D. R2D2 and Droid Army

An army ofNDroids is lined on one row. Each droid was described bymIntegers a1,? a 2,?...,? a m , where ai is the number of details of theI-th type in this droid ' s mechanism. R2-D2 wants to destroy the sequence of consecutive droids of maximum length. He hasmWeapons, theI-th weapon can affect all the droids in the army by destroying one detail of theI-th type (if the droid doesn ' t has the details of this type, nothing happens to it).

A Droid is considered to being destroyed when the all of it details are destroyed. R2-D2 can make at the most k shots. How many shots from the weapon of what type should r2-d2 do to destroy the sequence of consecutive droids of maximum Len Gth?

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.

NextNLines follow describing the droids. Each line containsmIntegers a1,? a 2,?...,? a m (0?≤? a i? ≤?108 ), where ai is the number of details of theI-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 the robot should make to destroy the subsequence of consecutive of the droids length.

If there is multiple optimal solutions, print any of them.

It is not a necessary to make exactly K shots, the number of shots can was less.

Sample Test (s) input

5 2 44 01 22 10 21 3

Output

2 2

Input

3 2 41 21 32 2

Output

1 3

Note

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

In the second test the first and second droids'll be destroyed.

Test instructions: There are n robots, each robot has m logo (used to express the attribute), R2D2 This weapon can hit k times, every dozen, all the corresponding properties of the robot will be reduced by 1, ask at least a few times, can make the continuous robot properties all become 0 of the length of the largest, the number of shots per property output.

Idea: It is obvious that the problem is to use a line segment tree to record the maximum value of each attribute in a continuous region (that is, in this interval to all the properties of the robot into 0 required to hit the number of times), in order to find the longest continuous region, we need to use two points, to avoid timeouts.

The code is as follows:

#include <cstdio> #include <cstring> #include <iostream> #include <algorithm>using namespace STD; #define L (x) (x<<1) #define R (x) (x<<1|1) #define MID (x, y) (x+y) >>1const int Maxn=1e5+10;int A[MAXN ][6], ans[6], Temp[6];__int64 k;int m,n;struct Node{int left, right, val[6];} Rob[4*maxn];void Build (int l, int r, int rt) {Rob[rt].left=l;rob[rt].right=r;if (l==r) {for (int i=1; i<=m; i++) {Rob[rt] . Val[i]=a[l][i];} return;} int Mid=mid (L,R); Build (L, Mid, L (RT)); Build (Mid+1, R, R (RT)), for (int i=1; i<=m; i++) {Rob[rt].val[i]=max (rob[l (RT)].val[i], rob[r (RT)].val[i]);}} int Query (int l, int r, int rt, int x) {if (L==rob[rt].left && r==rob[rt].right) {return rob[rt].val[x];} int max=0;if (l<=rob[l (RT)].right) {if (r<=rob[l (RT)].right) {max=query (l,r,l (RT), x);} Else{max=query (L,rob[l (RT)].right, L (RT), x);}} if (R>=rob[r (RT)].left) {if (L>=rob[r (RT)].left) {max=query (L,r,r (RT), x);} else Max=max (Max, Query (Rob[r (RT)].left, R, R (RT), x));} return Max;} BOOL OK (int mID) {bool flag=false;for (int i=1; i<=n-mid+1; i++) {int num=0;for (int j=1; j<=m; J + +) {temp[j]=query (I, I+mid-1, 1, j) ; num+=temp[j];} if (num<=k) {flag=true;memcpy (ans,temp,sizeof (temp)); Fill (temp, temp+6, 0);} if (flag) return True;else return false;} int main () {while (scanf ("%d%d%i64d", &n, &m, &k)!=eof) {for (Int. I=1; i<=n; i++) {for (int j=1; j<=m; J + +) { scanf ("%d", &a[i][j]);}}    Build (1,n,1);    int le=1, ri=n;    while (le<=ri) {int mid= (LE+RI)/2; if (OK (mid)) {le=mid+1;}    else ri=mid-1;    }//printf ("%d", ans[1]);    for (int i=1; i<m; i++) {printf ("%d", ans[i]); } printf ("%d\n", Ans[m]);}  return 0;}

Codeforces 514D R2D2 and Droid Army