You are given three integers a, b and x. Your task is to construct a binary string s of length n=a+b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1≤i<n) such that si≠si+1
. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices i
such that 1≤i<n and si≠si+1 (i=1,2,3,4). For the string "111001" there are two such indices i (i=3,5
).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.
Input
The first line of the input contains three integers a
, b and x (1≤a,b≤100,1≤x<a+b)
.
Output
Print only one string s
, where s
is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Examples
Input
2 2 1
Output
1100
Input
3 3 3
Output
101100
Input
5 3 6
Output
01010100
Note
All possible answers for the first example:
- 1100;
- 0011.
All possible answers for the second example:
- 110100;
- 101100;
- 110010;
- 100110;
- 011001;
- 001101;
- 010011;
- 001011.
#include<bits/stdc++.h>
using namespace std;
int main()
{int a,b,x,n,i,j;char s[1010];cin>>a>>b>>x;n=a+b;if(a>b){s[1]='0';a--;for(i=2;i<=x;i++){if(s[i-1]=='0'){s[i]='1';b--;}else{s[i]='0';a--;}}if(s[x]=='0'){for(i=x+1;;i++){if(a>0){s[i]='0';a--;}else{s[i]='1';b--;}if(a==0&&b==0)break;}}else{for(i=x+1;;i++){if(b>0){s[i]='1';b--;}else{s[i]='0';a--;}if(a==0&&b==0)break;}}}