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.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.Map.Entry;

public class Main {
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod = 1000000000 + 7;

	private StringBuilder ans_sb;
	private int sum = 0;

	private void soln() {
		int n = nextInt();
		int m = nextInt();
		int[] arr = nextIntArray(m);
		int[] ans = new int[n];
		Arrays.fill(ans, -1);
		boolean f = true;
		HashSet<Integer> anss = new HashSet<>();
		for(int i=1;i<m;i++) {
			int diff = arr[i] - arr[i - 1];
			if(diff <= 0)
				diff += n;
		//	debug(diff);
			if(ans[arr[i-1] - 1] == -1) {
				ans[arr[i-1] - 1] = diff;
				if(anss.contains(diff)) {
					f = false;
					pw.println(-1);
					break;
				}
				anss.add(diff);
			}else {
				if(ans[arr[i-1] - 1] != diff) {
					f = false;
					pw.println(-1);
					break;
				}
			}
		}
		if(f) {
			TreeSet<Integer> set = new TreeSet<>();
			for(int i=0;i<n;i++)
				set.add(i+1);
		//	debug(set);
			for(int i=0;i<n;i++) {
				if(ans[i] != -1) {
					set.remove(ans[i]);
				}
				
			//	set.remove(ans[i]);
			}
			for(int i=0;i<n;i++) {
				if(ans[i]==-1) {
					ans[i] = set.first();
					set.remove(ans[i]);
				}
				pw.print(ans[i]+" ");
			}
		}
	}
	private class Bridge {
		private LinkedList<Edge>[] graph;
		private LinkedList<Integer>[] tree;
		private int t;
		private boolean[] isBridge;
		private int[] cno;

		public Bridge(int n, int m) {
			pre(n, m);
		}

		private class Edge {
			int u, v, i;

			public Edge(int a, int b, int c) {
				u = a;
				v = b;
				i = c;
			}
		}

		private void pre(int n, int m) {
			graph = new LinkedList[n];
			tree = new LinkedList[n];
			for (int i = 0; i < m; i++) {
				int u = nextInt() - 1;
				int v = nextInt() - 1;
				Edge e = new Edge(u, v, i);
				graph[u].add(e);
				graph[v].add(e);
			}
			isBridge = new boolean[m];
			cno = new int[n];
			boolean[] v = new boolean[n];
			int[] arr = new int[n];
			for (int i = 0; i < n; i++)
				if (!v[i])
					dfs(i, null, v, arr);
		}

		private int dfs(int u, Edge e, boolean[] v, int[] arr) {
			v[u] = true;
			arr[u] = t++;
			int min = arr[u];
			Iterator<Edge> it = graph[u].listIterator();
			while (it.hasNext()) {
				Edge x = it.next();
				int w = x.u;
				if (x.u == u)
					w = x.v;
				if (!v[w])
					min = Math.min(min, dfs(w, x, v, arr));
				else if (x != e)
					min = Math.min(min, arr[w]);
			}
			if (min == arr[u] && e != null)
				isBridge[e.i] = true;
			return min;
		}

		private void bfs(int u, int cmpNo, Queue<Integer>[] q, boolean[] v) {
			int cur = cmpNo;
			cno[cur] = cmpNo;
			q[cur].add(u);
			v[u] = true;
			while (!q[cur].isEmpty()) {
				int x = q[cur].poll();
				Iterator<Edge> it = graph[x].listIterator();
				while (it.hasNext()) {
					Edge x1 = it.next();
					int w = x1.u;
					if (w == x)
						w = x1.v;
					if (!v[w]) {
						if (isBridge[x1.i]) {
							tree[cur].add(0, cmpNo + 1);
							tree[cmpNo + 1].add(0, cur);
							bfs(w, cmpNo + 1, q, v);
						} else {
							bfs(w, cmpNo, q, v);
						}
					}
				}
			}
		}
	}

	private String solveEqn(long a, long b) {
		long x = 0, y = 1, lastx = 1, lasty = 0, temp;
		while (b != 0) {
			long q = a / b;
			long r = a % b;
			a = b;
			b = r;
			temp = x;
			x = lastx - q * x;
			lastx = temp;
			temp = y;
			y = lasty - q * y;
			lasty = temp;
		}
		return lastx + " " + lasty;
	}

	private void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	private long pow(long a, long b, long c) {
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}

	private long gcd(long n, long l) {
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}

	public static void main(String[] args) throws Exception {
		new Thread(null, new Runnable() {
			@Override
			public void run() {
				new Main().solve();
			}
		}, "1", 1 << 25).start();
		// new Main().solve();
	}

	public StringBuilder solve() {
		InputReader(System.in);
		/*
		 * try { InputReader(new
		 * FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt")); }
		 * catch(FileNotFoundException e) {}
		 */
		pw = new PrintWriter(System.out);
		// ans_sb = new StringBuilder();
		soln();

		pw.close();
		// System.out.println(ans_sb);
		return ans_sb;
	}

	public void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private int nextInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private long nextLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private int[] nextIntArray(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private void pArray(long[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private char nextChar() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}