Mr. Chanek has a new game called Dropping Balls. Initially, Mr. Chanek has a grid a of size n × m

Each cell (x,y) contains an integer a_{x,y} denoting the direction of how the ball will move.

  * a_{x,y}=1 — the ball will move to the right (the next cell is (x, y + 1)); 
  * a_{x,y}=2 — the ball will move to the bottom (the next cell is (x + 1, y)); 
  * a_{x,y}=3 — the ball will move to the left (the next cell is (x, y - 1)). 



Every time a ball leaves a cell (x,y), the integer a_{x,y} will change to 2. Mr. Chanek will drop k balls sequentially, each starting from the first row, and on the c_1, c_2, ..., c_k-th (1 ≤ c_i ≤ m) columns.

Determine in which column each ball will end up in (position of the ball after leaving the grid).

Input

The first line contains three integers n, m, and k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 10^5) — the size of the grid and the number of balls dropped by Mr. Chanek.

The i-th of the next n lines contains m integers a_{i,1},a_{i,2},…,a_{i,m} (1 ≤ a_{i,j} ≤ 3). It will satisfy a_{i, 1} ≠ 3 and a_{i, m} ≠ 1.

The next line contains k integers c_1, c_2, …, c_k (1 ≤ c_i ≤ m) — the balls' column positions dropped by Mr. Chanek sequentially.

Output

Output k integers — the i-th integer denoting the column where the i-th ball will end.

Examples

Input


5 5 3
1 2 3 3 3
2 2 2 2 2
2 2 2 2 2
2 2 2 2 2
2 2 2 2 2
1 2 1


Output


2 2 1 


Input


1 2 2
1 3
1 2


Output


1 2 

Note

In the first example, the first ball will drop as follows. Note that the cell (1, 1) will change direction to the bottom direction.

<image>

The second and third balls will drop as follows. 

<image>

All balls will be dropped from the first row and on the c_1, c_2, ..., c_k-th columns respectively. A ball will stop dropping once it leaves the grid.
#define _CRT_SECURE_NO_WARNINGS

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <set>
#include <unordered_set>
#include <map>
#include <cmath>
#include <queue>
#include <iomanip>
#include <bitset>
#include <unordered_map>
#include <stack>
#include <memory.h>
#include <list>
#include <numeric>
#include <functional>
#include <complex>
#include <cassert>
#include <regex>
#include "windows.h"
#define ll long long
#define ld long double
#define ull unsigned ll

#define pii pair<int,int> 
#define pll pair<ll, ll>

#define vi vector<int>
#define vll vector<ll>
#define vpii vector<pii>
#define vpll vector<pll>
#define vvi vector<vector<int>>
#define vvll vector<vector<ll>>
#define vs vector<string>

#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()

#define forn(it,from,to) for(int (it)=from; (it)<to; (it)++)
#define ford(it,from,to) for(int (it)=from; (it)>=to; (it)--)
#define fors(it,from,to,step) for(int (it)=from; (it)<to; (it)+=step)
#define fora(it,v) for(auto&(it) : v)

#define yes cout << "yes\n"
#define no cout << "no\n"

using namespace std;



int main() {
#ifdef _DEBUG
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#else
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
#endif
	ios::sync_with_stdio(false);
	cin.tie(0); cout.tie(0);
	cout.setf(ios::fixed); cout.precision(20);
		

	int n, m, k;
	cin >> n >> m >> k;
	vector<vector<pair<int,int>>> v(n, vector<pair<int, int>>(m));

	forn(i, 0, n) {
		forn(j, 0, m) {
			int x;
			cin >> x;
			if (x == 2) {
				v[i][j] = { 1,0 };
			}
			else if (x == 1) {
				v[i][j] = { 0,1 };
			}
			else if (x == 3) {
				v[i][j] = { 0,-1 };
			}
		}
	}
	vector<int>p(m);
	for (int i = 0; i < k; i++) {
		int x;
		cin >> x;
		x--;
		pair<int, int>coord = { 0,x };
		coord.first = p[x];
		while (coord.first != n) {
			pair<int, int>pr = v[coord.first][coord.second];
			if (coord.first - 1 == p[coord.second]) {
				p[coord.second]++;
			}
			v[coord.first][coord.second] = { 1,0 };
			coord.first += pr.first;
			coord.second += pr.second;
		}
		cout << coord.second + 1 << " ";
	}



	return 0;

}