CF288A.Polo the Penguin and Strings

普及/提高-

通过率:0%

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题目描述

Little penguin Polo adores strings. But most of all he adores strings of length nn .

One day he wanted to find a string that meets the following conditions:

  1. The string consists of nn lowercase English letters (that is, the string's length equals nn ), exactly kk of these letters are distinct.
  2. No two neighbouring letters of a string coincide; that is, if we represent a string as s=s1s2... sns=s_{1}s_{2}...\ s_{n} , then the following inequality holds, s_{i}≠s_{i+1}(1<=i<n) .
  3. Among all strings that meet points 1 and 2, the required string is lexicographically smallest.

Help him find such string or state that such string doesn't exist.

String x=x1x2... xpx=x_{1}x_{2}...\ x_{p} is lexicographically less than string y=y1y2... yqy=y_{1}y_{2}...\ y_{q} , if either p<q and x1=y1,x2=y2,... ,xp=ypx_{1}=y_{1},x_{2}=y_{2},...\ ,x_{p}=y_{p} , or there is such number rr (r<p,r<q) , that x1=y1,x2=y2,... ,xr=yrx_{1}=y_{1},x_{2}=y_{2},...\ ,x_{r}=y_{r} and x_{r+1}<y_{r+1} . The characters of the strings are compared by their ASCII codes.

输入格式

A single line contains two positive integers nn and kk (1<=n<=106,1<=k<=26)(1<=n<=10^{6},1<=k<=26) — the string's length and the number of distinct letters.

输出格式

In a single line print the required string. If there isn't such string, print "-1" (without the quotes).

输入输出样例

  • 输入#1

    7 4
    

    输出#1

    ababacd
    
  • 输入#2

    4 7
    

    输出#2

    -1
    
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