#include <iostream>
#include <cstdio>
#include <string>
#include <algorithm>
#include <cmath>
#include <vector>
#include <cstring>
#include <cstdlib>
using namespace std;

const int maxn = 50000;
int is_prime[maxn];
int prime[maxn];
int vis[maxn];
int cnt;

//预处理素数表
void init() {
    memset( vis, 0, sizeof( vis ) );
    memset( is_prime, 0, sizeof( is_prime ) );
    is_prime[0] = is_prime[1] = 1;
    int i, j;

    for ( i = 2; i < maxn; i++ ) {
        for ( j = 2; j * i < maxn; j++ )
            is_prime[i * j] = 1;
    }

    cnt = 0;

    for ( i = 2; i < maxn; i++ ) {
        if ( !is_prime[i] )
            prime[cnt++] = i;
    }
}

int find( int key ) {
    int left = 0, right = cnt - 1;

    while ( left <= right ) {
        int mid = ( left + right ) >> 1;

        if ( prime[mid] == key ) return key;
        else if ( prime[mid] < key )  left = mid + 1;
        else right = mid - 1;
    }

    return prime[left];
}

string str[105];
int pos[105];
int main() {
    init();
    int m_size, n, e, i, j, h;
    cin >> m_size >> n;

    if ( is_prime[m_size] )
        m_size = find( m_size );

    vector<int> ans;

    for ( i = 0; i < n; i++ ) {
        cin >> e;
        h = e % m_size;

        if ( !vis[h] ) {
            ans.push_back( h );
            vis[h] = 1;
        } else {
            int ok = 0;
            //二次探测 quadrtic probing
            for ( j = 1; j <= (m_size+1)>>1; j++ ) {
                h = ( e + j*j ) % m_size;

                if ( !vis[ h ] ) {
                    ans.push_back( h );
                    vis[h] = 1;
                    ok = 1;
                    break;
                }
            }

            if( !ok ) ans.push_back( -1 );
        }
    }

    if ( !ans.empty() )
        cout << ans[0];

    for ( i = 1; i < ans.size(); i++ ) {
        cout << " ";

        if ( ans[i] == -1 )   cout << "-";
        else cout << ans[i];
    }

    cout << endl;
    return 0;
}