5298: Stack

内存限制:256 MB 时间限制:1.000 S
评测方式:文本比较 命题人:
提交:1 解决:0

题目描述


ZYT had a magic permutation a1,a2,⋯,ana_1,a_2,\cdots, a_na1,a2,,an, and he constructed a sequence b1,b2,⋯bnb_1,b_2,\cdots b_nb1,b2,bn by the following pseudo code:


Stk is an empty stack
for i = 1 to n :
   while ( Stk is not empty ) and ( Stk's top > a[i] ) :
       pop Stk
   push a[i]
   b[i]=Stk's size

But he somehow forgot the permutation a, and only got some k elements of bi.

Construct a permutation a satisfying these bi , or determine no such permutation exists.

Here a permutation refers to a sequence that contains all integers from 1 to n exactly once.



输入


he first line contains two integers n,k(1≤k≤n) the length of the permutation, the number of left bi.
Then k lines each contains two integer pi,xi, denoting that bpi=xi.

输出


Output one line with n integers a1,a2,⋯an— a possible permutation.
If no such permutation exists, output one integer -1.

样例输入 复制

5 2
2 2
5 4

样例输出 复制

1 2 5 3 4

提示


It's guaranteed that n≤106,1≤pi,xi≤n and ∀i≠j,pi≠pj.