CF932C.Permutation Cycle

普及/提高-

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题目描述

For a permutation P[1... N]P[1...\ N] of integers from 11 to NN , function ff is defined as follows:

Let g(i)g(i) be the minimum positive integer jj such that f(i,j)=if(i,j)=i . We can show such jj always exists.

For given N,A,BN,A,B , find a permutation PP of integers from 11 to NN such that for 1<=i<=N1<=i<=N , g(i)g(i) equals either AA or BB .

输入格式

The only line contains three integers N,A,BN,A,B ( 1<=N<=106,1<=A,B<=N1<=N<=10^{6},1<=A,B<=N ).

输出格式

If no such permutation exists, output -1. Otherwise, output a permutation of integers from 11 to NN .

输入输出样例

  • 输入#1

    9 2 5
    

    输出#1

    6 5 8 3 4 1 9 2 7
  • 输入#2

    3 2 1
    

    输出#2

    1 2 3 

说明/提示

In the first example, g(1)=g(6)=g(7)=g(9)=2g(1)=g(6)=g(7)=g(9)=2 and g(2)=g(3)=g(4)=g(5)=g(8)=5g(2)=g(3)=g(4)=g(5)=g(8)=5

In the second example, g(1)=g(2)=g(3)=1g(1)=g(2)=g(3)=1

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