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 PYTHON3):

Solution:
"""
Author    : co_devil Chirag Garg
Institute : JIIT
"""


from __future__ import division, print_function
from sys import stdin,stdout
import itertools, os, sys, threading
from collections import deque, Counter, OrderedDict, defaultdict
import heapq
from math import ceil,floor,log,sqrt,factorial,pow,pi,gcd
# from bisect import bisect_left,bisect_right
# from decimal import *,threading
"""from io import BytesIO, IOBase
if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip
else:
    from builtins import str as __str__
    str = lambda x=b'': x if type(x) is bytes else __str__(x).encode()
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
    def __init__(self, file):
        self._buffer = BytesIO()
        self._fd = file.fileno()
        self._writable = 'x' in file.mode or 'r' not in file.mode
        self.write = self._buffer.write if self._writable else None

    def read(self):
        return self._buffer.read() if self._buffer.tell() else os.read(self._fd, os.fstat(self._fd).st_size)

    def readline(self):
        while self.newlines == 0:
            b, ptr = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE)), self._buffer.tell()
            self._buffer.seek(0, 2), self._buffer.write(b), self._buffer.seek(ptr)
            self.newlines += b.count(b'\n') + (not b)
        self.newlines -= 1
        return self._buffer.readline()

    def flush(self):
        if self._writable:
            os.write(self._fd, self._buffer.getvalue())
            self._buffer.truncate(0), self._buffer.seek(0)
sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
input = lambda: sys.stdin.readline().rstrip(b'\r\n')

def print(*args, **kwargs):
    sep, file = kwargs.pop('sep', b' '), kwargs.pop('file', sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop('end', b'\n'))
    if kwargs.pop('flush', False):
        file.flush()

"""


def ii(): return int(input())
def si(): return str(input())
def mi(): return map(int,input().split())
def li(): return list(mi())

def fii(): return int(stdin.readline())
def fsi(): return str(stdin.readline())
def fmi(): return map(int,stdin.readline().split())
def fli(): return list(fmi())


abc = 'abcdefghijklmnopqrstuvwxyz'
abd = {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12,
       'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24,
       'z': 25}
mod = 1000000007
dx, dy = [-1, 1, 0, 0], [0, 0, 1, -1]
def getKey(item): return item[0]
def sort2(l): return sorted(l, key=getKey)
def d2(n, m, num): return [[num for x in range(m)] for y in range(n)]
def isPowerOfTwo(x): return (x and (not (x & (x - 1))))
def decimalToBinary(n): return bin(n).replace("0b", "")
def ntl(n): return [int(i) for i in str(n)]
def powerMod(x, y, p):
    res = 1
    x %= p
    while y > 0:
        if y & 1:
            res = (res * x) % p
        y = y >> 1
        x = (x * x) % p
    return res
def gcd(x, y):
    while y:
        x, y = y, x % y
    return x
# For getting input from input.txt file
# sys.stdin = open('input.txt', 'r')

# Printing the Output to output.txt file
# sys.stdout = open('output.txt', 'w')

graph = defaultdict(list)
visited = [0] * 1000000
col = [-1] * 1000000
def dfs(v, c):
    if visited[v]:
        if col[v] != c:
            print('-1')
            exit()
        return
    col[v] = c
    visited[v] = 1
    for i in graph[v]:
        dfs(i, c ^ 1)

def bfs(d,v):
    q=[]
    q.append(v)
    visited[v]=1
    while len(q)!=0:
        x=q[0]
        q.pop(0)
        for i in d[x]:
            if visited[i]!=1:
                visited[i]=1
                q.append(i)
        print(x)
    print(l)

def make_graph(e):
    d={}
    for i in range(e):
        x,y=mi()
        if x not in d.keys():
            d[x]=[y]
        else:
            d[x].append(y)
        if y not in d.keys():
            d[y] = [x]
        else:
            d[y].append(x)
    return d
def gr2(n):
    d={}
    for i in range(n):
        x,y=mi()
        if x not in d.keys():
            d[x]=[y]
        else:
            d[x].append(y)
    return d

def connected_components(graph):
    seen = set()
    def dfs(v):
        vs = set([v])
        component=[]
        while vs:
            v = vs.pop()
            seen.add(v)
            vs |= set(graph[v]) - seen
            component.append(v)
        return component
    ans=[]
    for v in graph:
        if v not in seen:
            d=dfs(v)
            ans.append(d)
    return ans

n, m = mi()
l = li()
a = [None] * n
c = set(range(1, n + 1))
for i in range(m - 1):
    j = l[i] - 1
    d = l[i + 1] - l[i]
    if d <= 0:
        d += n
    if a[j] != d:
        if a[j] or d not in c:
            print(-1)
            exit()
        a[j] = d
        c.remove(d)
for i in range(n):
    if not a[i]:
        a[i] = c.pop()
print(*a)