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.
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair<int, int> pi;
typedef pair<ll, ll> pll;
#define m7 1000000007
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define rep(i,a,b) for(int i=a; i<b; i++)
#define forn(n) for(int i=0; i<n; i++)

void fastIO(){ ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); }

bool pof2(int n){ if(n & n-1) return false; return true; }

int main() {

    fastIO();

    

        int n, m, k; cin >> n >> m >> k;
        int a[n][m];
        int b[k];
        int c[m] = {};

        rep(i,0,n)
            rep(j,0,m){
                cin >> a[i][j];
                if(a[i][j] == 2)
                    c[j]++;
            }

        forn(k){
            cin >> b[i];
            b[i]--;
        }

        int ans[n];
        forn(k){
            int x = 0, y = b[i];
            if(c[y] == n)
                ans[i] = y;
            else{
                while(x < n){
                    if(a[x][y] == 1){
                        a[x][y] = 2;
                        c[y]++;
                        y += 1;
                    }
                    else if(a[x][y] == 3){
                        a[x][y] = 2;
                        c[y]++;
                        y -= 1;
                    }
                    else
                        x += 1;
                }
                ans[i] = y;
            }
        }

        forn(k)
            cout << ans[i] + 1 << ' ';
        cout << endl;
    
}