Problem: n children are standing in a circle and playing a game. Children's numbers in clockwise order form a permutation a1, a2, ..., an of length n. It is an integer sequence such that each integer from 1 to n appears exactly once in it.

The game consists of m steps. On each step the current leader with index i counts out ai people in clockwise order, starting from the next person. The last one to be pointed at by the leader becomes the new leader.

You are given numbers l1, l2, ..., lm — indices of leaders in the beginning of each step. Child with number l1 is the first leader in the game. 

Write a program which will restore a possible permutation a1, a2, ..., an. If there are multiple solutions then print any of them. If there is no solution then print -1.

Input

The first line contains two integer numbers n, m (1 ≤ n, m ≤ 100).

The second line contains m integer numbers l1, l2, ..., lm (1 ≤ li ≤ n) — indices of leaders in the beginning of each step.

Output

Print such permutation of n numbers a1, a2, ..., an that leaders in the game will be exactly l1, l2, ..., lm if all the rules are followed. If there are multiple solutions print any of them. 

If there is no permutation which satisfies all described conditions print -1.

Examples

Input

4 5
2 3 1 4 4


Output

3 1 2 4 


Input

3 3
3 1 2


Output

-1

Note

Let's follow leadership in the first example: 

  * Child 2 starts. 
  * Leadership goes from 2 to 2 + a2 = 3. 
  * Leadership goes from 3 to 3 + a3 = 5. As it's greater than 4, it's going in a circle to 1. 
  * Leadership goes from 1 to 1 + a1 = 4. 
  * Leadership goes from 4 to 4 + a4 = 8. Thus in circle it still remains at 4. 

Solution (in JAVA):

Solution:
                                    import java.util.*; 
                                    import java.math.*;
                                    import java.io.*;
                                    import java.text.DecimalFormat;
                                    import java.math.BigInteger;
                                    public class Main{
                                        //static int d=20;
                                        static long mod=1000000007 ;
                                        
                                        static ArrayList<ArrayList<Edge>> arr;
                                       // static long[] dp1,dp2;
                                        static int[] a;
                                        static int[] vis,num;
                                        static long max;
                                        static HashSet<String> hs;
                                        //static int flag,ans;
                                        static long max1,max2,ans1;
                                        
                                        static int flag=0;
                                        static int[] tin,tout,parent,level;
                                        static HashMap<Long,Integer> hm;
                                        static long[] dp1,dp2,dp3,dp4;
                                        static int ct=0;
                                           
                                        public static void main(String[] args)  throws IOException {
                                            ///long start=System.currentTimeMillis();
                                            boolean online =false  ;
                                            String fileName = "C-large-practice";
                                            PrintWriter out; 
                                            if (online) {
                                                s.init(new FileInputStream(new File("Downloads/"+fileName + ".in")));
                                                 out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                            }
                                             else {
                                                s.init(System.in);   
                                            
                                                out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
                                                //out= new PrintWriter(new FileWriter(fileName + "out.txt"));
                                            }//r,b,y,g
                                            int n,m;
                                            n=s.ni();
                                            m=s.ni();
                                            int[] l=new int[m];
                                            for(int i=0;i<m;i++)
                                                l[i]=s.ni();
                                            int[] a=new int[n];
                                            Arrays.fill(a,-1);
                                            int flag=0;
                                            HashSet<Integer> hs=new HashSet<>();
                                            for(int i=0;i<m-1;i++){
                                                int x=(l[i+1]-l[i]+n)%n;
                                                if(x==0){
                                                    x=n;

                                                }
                                                int y=l[i]-1;
                                                if(hs.contains(x) && a[y]!=x){
                                                    flag=1;
                                                    break;
                                                }
                                                else if(a[y]!=-1 && a[y]!=x ){
                                                    flag=1;
                                                    break;
                                                }
                                                else{
                                                    a[y]=x;
                                                    hs.add(x);
                                                }

                                            }
                                            ArrayList<Integer> arr=new ArrayList<>();
                                            for(int i=1;i<=n;i++){
                                                if(!hs.contains(i)){
                                                    arr.add(i);
                                                }
                                            }
                                            for(int i=0;i<n;i++){
                                                if(a[i]==-1){
                                                    if(arr.size()>0){
                                                        int x=arr.get(0);
                                                        a[i]=x;
                                                        arr.remove(0);
                                                    }
                                                    else{
                                                        flag=1;
                                                        break;
                                                    }
                                                }

                                            }
                                            if(flag==1)
                                                out.println(-1);
                                            else{
                                                for(int x:a)
                                                    out.print(x+" ");
                                                out.println();
                                            }
                                            out.close();    
                                    
                                        }   
                                      
                                     
                                        public static int gcd(int a, int b){
                                                if (a == 0) return b;
                                                return gcd(b % a, a);
                                        }
                                            
                                        public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
                                            vis[c]=1;
                                            if(g!=-1){
                                                if(!arr.get(c).contains(g)){
                                                    flag=1;
                                                    return;
                                                }
                                            }
                                            for(int x:arr.get(c)){
                                                if(x!=p && x!=g && vis[x]==0 ){
                                                    cfs(arr,x,c,p,vis);
                                                }
                                            }
 
                                        }
                                                              //   public static void dfs(int u,int p){
         //                            //       if(p>=0)
         //                            //           tin[u]=tout[u]=tt++;
         //                            //       if(p>=0)
         //                            //           level[u]=level[p]+1;
         //                            //       parent[u]=p;
         //                            //       for(int x:arr.get(u)){
         //                            //           if(x!=p){
         //                            //               dfs(x,u);
         //                            //               tout[u]=Math.max(tout[u],tout[x]);
         //                            //           }
         //                            //       }
         //                            //       
         //
         //
                                     //   }
                                        public static int lca(int[][] p,int a,int b){
                                            if(level[a]<level[b]){
                                                int x=a;
                                                a=b;
                                                b=x;
                                            }
                                            int log=p[0].length;
                                            for(int i=log-1;i>=0;i--){
                                                if(1<<i<=level[a]-level[b]){
                                                    a=p[a][i];
                                                }
                                            }
                                            if(a==b)
                                                return a;
                                            for(int i=log-1;i>=0;i--){
                                                if(p[a][i]!=p[b][i]){
                                                    a=p[a][i];
                                                    b=p[b][i];
                                                }
                                            }
                                            return p[a][0];
         
                                        }
                                        public static int[][] par(int[] parent){
                                            int n=arr.size();
                                            int[][] p=new int[n][17];
                                            for(int i=0;i<n;i++)
                                                p[i][0]=parent[i];
                                            for(int k=1;k<17;k++){
                                                for(int i=0;i<n;i++){
                                                    if(p[i][k-1]>-1)
                                                        p[i][k]=p[p[i][k-1]][k-1];
                                                    else
                                                        p[i][k]=-1;
                                                }
                                            }
                                            return p;
                                        }
                                        static class Edge {
                                               int from;
                                                int to;
                                                int cost;
                                        
                                               public Edge(int from, int to, int weight) {
                                                   this.from = from;
                                                   this.to = to;
                                                   this.cost= weight;
                                               }
                                        }                               
                                        static class Node {
                                            int start;
                                            int end;
                        
                                            int cost;
                                            int updated;
                        
                                            Node[] nodes;
                        
                                            public Node(int start, int end) {
                                                this.start = start;
                                                this.end = end;
                        
                                                if (start < end) {
                                                    int[] pos = {start, (start + end) / 2, end};
                                                    nodes = new Node[2];
                                                    for (int i = 0; i < 2; i++) {
                                                        nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                                                    }
                                                }
                                            }
                        
                                            public void update(int queryStart, int queryEnd, int value) {
                                                if (queryEnd < start || end < queryStart) {
                                                    return;
                                                }
                        
                                                if (queryStart <= start && end <= queryEnd) {
                                                    cost += value;
                                                    updated += value;
                                                    return;
                                                }
                        
                                                propagate();
                                                for (Node node: nodes) {
                                                    node.update(queryStart, queryEnd, value);
                                                }
                                            }
                        
                                            public int query(int pos) {
                                                if (pos < start || end < pos) {
                                                    return 0;
                                                }
                        
                                                if (start == end) {
                                                    return cost;
                                                }
                        
                                                propagate();
                                                int ans = 0;
                                                for (Node node: nodes) {
                                                    ans = Math.max(ans, node.query(pos));
                                                }
                                                return ans;
                                            }
                        
                                            public void propagate() {
                                                if (updated != 0 && start < end) {
                                                    for (Node node: nodes) {
                                                        node.cost += updated;
                                                        node.updated += updated;
                                                    }
                                                    updated = 0;
                                                }
                                            }
                                        }
                                        public static double nthroot(int n, double A) {
                                            return nthroot(n, A, 0.0000001);
                                        }
                                        public static double nthroot(int n, double A, double p) {
                                            if(A < 0) {
                                                System.err.println("A < 0");// we handle only real positive numbers
                                                return -1;
                                            } else if(A == 0) {
                                                return 0;
                                            }
                                            double x_prev = A;
                                            double x = A / n;  // starting "guessed" value...
                                            while(Math.abs(x - x_prev) > p) {
                                                x_prev = x;
                                                x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
                                            }
                                            return x;
                                        }
                                        
                                        static class item implements Comparable<item> {
                                            int beauty,cost,id;
                                            public item(int x,int y,int z){
                                                id=x;
                                                beauty=y;
                                                cost=z;
                                                
                                            }
                                            public int compareTo(item o){
                                                return  o.beauty-beauty;
                                            }
                                            
                                        }
                                       
                                        public static void dfs2(int c,int p,int[] a){
                                            //System.out.println(c+" "+p);
                                           
                                            
                                            
                 
                                        }
        //public static void dfs(int x,int[] vis,Stack<Integer> st){
                                        //    vis[x]=1;
                                        //    ArrayList<Integer> arr2=arr.get(x);
                                        //    Collections.sort(arr2);
                                        //    for(int i=arr2.size()-1;i>=0;i--){
                                        //        int z=arr2.get(i);
                                        //        if(vis[z]==0)
                                        //            dfs(z,vis,st);
                                        //    }
                                        //    st.push(x);
                 //
                                        //}
                                        public static long gcd(long a, long b){
                                                if (a == 0) return b;
                                                return gcd(b % a, a);
                                        }
                                            
                                        public static boolean check(long x){
                                            if(x%4==0 || x%7==0 || x%11==0)
                                                return true;
                                            if(x<4 || x<7 || x<11)
                                                return false;
                                            if(x%2==0){
                                                return check(x/2);
                                            }
                                            else
                                                return check(x/2) && check((x+1)/2);
                                        }
                                        public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
                                            long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
                                            if(val<0)
                                                return 1;
                                            else if(val>0)
                                                return -1;
                                            else
                                                return 0;
                                        }
                                        
                                        static class BIT{
                                        
                                            int N;
                                            long tree[];
                                            
                                            BIT(int N){
                                                this.N = N;
                                                tree = new long[N + 1];
                                            }
                                            
                                            void update(int idx,long val){
                                                while(idx <= N){
                                                    tree[idx]+=val;
                                                    idx += (idx & -idx);
                                                }
                                            }
                                            
                                            long query(int l,int r){
                                                if(l == 1)
                                                    return read(r);
                                                else
                                                    return read(r) - read(l-1);
                                            }
                                            
                                            long read(int idx){
                                                long sum = 0;
                                                while(idx > 0){
                                                    sum += tree[idx];
                                                    idx -= (idx & -idx);
                                                }
                                                return sum;
                                            }
                                        }
                                        public static boolean pal(String a){
                                            int i=0;
                                            int j=a.length()-1;
                                            while(i<j){
                                                if(a.charAt(i)!=a.charAt(j)){
                                                    return false;
                                                }
                                                i++;
                                                j--;
                                            }
                                            return true;
                                                
                                        }
                                        public static long find(long n,long k){
                                            if(n==2){
                                                if(k==1 || k==3)
                                                    return 1;
                                                else
                                                    return 2;
                                            }
                                            long t=pow2(2,n,mod)-1;
                                            long z=(t+1)/2;
                                            if(k==z)
                                                return n;
                                            if(k<z)
                                                return find(n-1,k);
                                            else
                                                return find(n-1,k-z);
                                        }
                                        public static long pow2(long a,long b,long mod){
                                                
                                                long ans=1;
                                               // long z=b;
                                                while(b>0){
                                                   
                                                    if(b%2==1)
                                                        ans=(a*ans)%mod;
                                                    a=(a*a)%mod;
                                                    b/=2;
                                                }
                                              
                                                return  ans;
                                        }
                                         public static long pow3(long a,long b){
                                                
                                                long ans=1;
                                               // long z=b;
                                                while(b>0){
                                                   
                                                    if(b%2==1)
                                                        ans=(a*ans);
                                                    a=(a*a);
                                                    b/=2;
                                                }
                                              
                                                return  ans;
                                        }
                                        public static long fib(long n){
                                            long[][]    f=new long[][]{{1L,1L},{1L,0}};
                                            if(n==0)
                                                return 0;
                                            f=arrpow(f,n-1);
                                            return f[0][0];
                                        }
                                        public static long[][] arrpow(long[][] a,long b){
                                           
                                                int n=a.length;
                                              //  long z=b;
                                                long[][] ans=new long[n][n];
                                                for(int i=0;i<n;i++)
                                                    ans[i][i]=1L;
                                                while(b>0){
                                                    
                                                    if(b%2==1)
                                                        ans=mul(a,ans);
                                                    a=mul(a,a);
                                                    b/=2;
                                                }
                                                
                                                return  ans;
                                        }
                                        public static long[][] mul(long[][] a,long[][] b){
                                            int n=a.length;
                                            int m=b[0].length;
                                            long[][] ans=new long[n][m];
                                            if(n==2 && m==2 && b.length==2){
                                                ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
                                                ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
                                                ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
                                                ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
                                                return ans;
             
                                            }
                                            for(int i=0;i<n;i++){
                                                for(int j=0;j<m;j++){
                                                    for(int k=0;k<b.length;k++){
                                                        ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                                                    }
                                                }
                                            }
                                            return ans; 
                                        }
                                         static class name implements Comparable<name> {
                                            long l,b,h;
                                            public name(long   x,long y,long z){
                                                {
                                                    l=x;
                                                    b=y;        
                                                }
                                                
                                                
                                                h=z;
                                            }
                                            public int compareTo(name o){
                                                return -(int)(l*b-o.l*o.b);
                                            }
                                            
                                        }
                                        public static class s {
                                            static BufferedReader reader;
                                            static StringTokenizer tokenizer;
                                        
                                            /** call this method to initialize reader for InputStream */
                                            static void init(InputStream input) {
                                                reader = new BufferedReader(
                                                            new InputStreamReader(input) );
                                                tokenizer = new StringTokenizer("");
                                            }   
                                        
                                            /** get next word */
                                            static String ns() throws IOException {
                                                while ( ! tokenizer.hasMoreTokens() ) {
                                                    //TODO add check for eof if necessary
                                                    tokenizer = new StringTokenizer(
                                                        reader.readLine() );
                                                }
                                                return tokenizer.nextToken();
                                            }
                                        
                                            static int ni() throws IOException {
                                                return Integer.parseInt( ns() );
                                            }
                                        
                                            static double nd() throws IOException {
                                                return Double.parseDouble( ns() );
                                            }
                                            static long nl() throws IOException {
                                                return Long.parseLong( ns() );
                                            }
                                        }
                                    }