// Author: Moulik
// Date Created: 23 February 2021
// Filename: D.cpp
#include <bits/stdc++.h>
using namespace std;
#ifdef _DEBUG
#define what_is(x) cerr << "DEBUG::BEGIN\n\tVariable name:\n\t\t" << #x << "\n\tdata:\n\t\t" << x << "\nDEBUG::END" << endl;
#else
#define what_is(x) ;
#endif

// CUSTOM FUNCTIONS

// Power using binary exponentation
long long power(long long base, int exponent){ 
    long long ans = 1;
    while(exponent > 0){ 
        if (exponent&1) 
            ans = (ans*base); 
        exponent >>= 1;
        base = base*base;
    }
    return ans; 
} 

// Power modulo p using binary exponentation
long long power(long long base, int exponent, int p){ 
    long long ans = 1;
    base = base%p;
    while(exponent > 0){ 
        if (exponent&1) 
            ans = (ans*base)%p; 
        exponent >>= 1;
        base = (base * base) % p; 
    } 
    return ans; 
}

// Return n^-1%p, given p is prime
int modInverse(int n, int p){
    return power(n,p-2,p);
}

// calculates factorial from 0 to n (inclusive)
void factorialCalc(vector<int> & factorial, int n){
    if(factorial.size()!=n+1){factorial.resize(n+1);}
    factorial[0]=1;
    factorial[1]=1;
    for(int i = 2; i <=n; i++){
        factorial[i] = factorial[i-1]*i;
    }
}

// calculates factorial mod p from 0 to n (inclusive) 
void factorialCalc(vector<int> & factorial, int n, int p){
    if(factorial.size()!=n+1){factorial.resize(n+1);}
    factorial[0]=1;
    factorial[1]=1;
    for(int i = 2; i <=n; i++){
        factorial[i] = (factorial[i-1]*1ll*i)%(p);
    }
}

// calculates nCr mod p, using fermats method, given p is prime.
unsigned long long nCr(unsigned long long n, int r, int p, vector<int> & fac){ 
    if (r == 0) 
        return 1; 
    return (1ll*fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) % p; 
}

// Sorts array in the given order {key is 0 indexed}
template <typename T>
void keySort(vector<T> &arr, vector<int> &key){
    int n = arr.size();
    if(key.size()!=n){
        throw runtime_error("Size of data array not equals to size of key array");
    }
    vector<T> ans(n);
    int ar[n];
    for(int i = 0; i < n; i++){
        ar[key[i]]=i;
    }
    for(int i = 0; i < n; i++){
        ans[i] = arr[ar[i]];
    }
    arr = ans;
}

#define rprint(data) std::cout << data;return  
#define rprintln(data) std::cout << data << endl;return  

#define selfMin(x, y) x=std::min(x,y);
#define selfMax(x, y) x=std::max(x,y);

// OSTREAMS

template<typename T1, typename T2>
ostream & operator<<(ostream &os, const pair<T1,T2> p){
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}

template<typename T>
ostream & operator<<(ostream &os, const vector<T> p){
    os << "{ ";
    for(auto i:p){
        os << i << ",";
    }
    os << "\b";
    os << "}";
    return os;
}

// ISTREAMS

template<typename T1, typename T2>
istream & operator >> (istream &in, pair<T1,T2> & p){
    in >> p.first >> p.second;
    return in;
}

void solve();

int main(){
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    solve();
    return 0;
}


void solve(){
    int a, b, k;
    cin >> a >> b >> k;
    if((a==0 || b==1)){
        if(k==0){
            cout << ("YES") << endl;
            cout << string(b, '1')+string(a, '0') << endl;
            cout << string(b, '1')+string(a, '0') << endl;
            return ;
        }
        else{
            rprintln("NO");
        }

    }
    if(k>a+b-2){
        rprintln("NO");
    }
    cout << "YES" << endl;

    string ans = "1" + string(b-1, '1') + string(a, '0');
    string base = ans;

    int lco = b-1;

    swap(ans[lco], ans[lco+min(k,a)]);
    k-=min(k,a);
    if(k==0){
        cout << base << endl;
        rprintln(ans);
    }
    swap(ans[lco], ans[lco-k]);
    cout << base << endl;
    rprintln(ans);


}

### Prompt

Construct a cpp code solution to the problem outlined:

You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

### Response

```cpp
// Author: Moulik
// Date Created: 23 February 2021
// Filename: D.cpp
#include <bits/stdc++.h>
using namespace std;
#ifdef _DEBUG
#define what_is(x) cerr << "DEBUG::BEGIN\n\tVariable name:\n\t\t" << #x << "\n\tdata:\n\t\t" << x << "\nDEBUG::END" << endl;
#else
#define what_is(x) ;
#endif

// CUSTOM FUNCTIONS

// Power using binary exponentation
long long power(long long base, int exponent){ 
    long long ans = 1;
    while(exponent > 0){ 
        if (exponent&1) 
            ans = (ans*base); 
        exponent >>= 1;
        base = base*base;
    }
    return ans; 
} 

// Power modulo p using binary exponentation
long long power(long long base, int exponent, int p){ 
    long long ans = 1;
    base = base%p;
    while(exponent > 0){ 
        if (exponent&1) 
            ans = (ans*base)%p; 
        exponent >>= 1;
        base = (base * base) % p; 
    } 
    return ans; 
}

// Return n^-1%p, given p is prime
int modInverse(int n, int p){
    return power(n,p-2,p);
}

// calculates factorial from 0 to n (inclusive)
void factorialCalc(vector<int> & factorial, int n){
    if(factorial.size()!=n+1){factorial.resize(n+1);}
    factorial[0]=1;
    factorial[1]=1;
    for(int i = 2; i <=n; i++){
        factorial[i] = factorial[i-1]*i;
    }
}

// calculates factorial mod p from 0 to n (inclusive) 
void factorialCalc(vector<int> & factorial, int n, int p){
    if(factorial.size()!=n+1){factorial.resize(n+1);}
    factorial[0]=1;
    factorial[1]=1;
    for(int i = 2; i <=n; i++){
        factorial[i] = (factorial[i-1]*1ll*i)%(p);
    }
}

// calculates nCr mod p, using fermats method, given p is prime.
unsigned long long nCr(unsigned long long n, int r, int p, vector<int> & fac){ 
    if (r == 0) 
        return 1; 
    return (1ll*fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) % p; 
}

// Sorts array in the given order {key is 0 indexed}
template <typename T>
void keySort(vector<T> &arr, vector<int> &key){
    int n = arr.size();
    if(key.size()!=n){
        throw runtime_error("Size of data array not equals to size of key array");
    }
    vector<T> ans(n);
    int ar[n];
    for(int i = 0; i < n; i++){
        ar[key[i]]=i;
    }
    for(int i = 0; i < n; i++){
        ans[i] = arr[ar[i]];
    }
    arr = ans;
}

#define rprint(data) std::cout << data;return  
#define rprintln(data) std::cout << data << endl;return  

#define selfMin(x, y) x=std::min(x,y);
#define selfMax(x, y) x=std::max(x,y);

// OSTREAMS

template<typename T1, typename T2>
ostream & operator<<(ostream &os, const pair<T1,T2> p){
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}

template<typename T>
ostream & operator<<(ostream &os, const vector<T> p){
    os << "{ ";
    for(auto i:p){
        os << i << ",";
    }
    os << "\b";
    os << "}";
    return os;
}

// ISTREAMS

template<typename T1, typename T2>
istream & operator >> (istream &in, pair<T1,T2> & p){
    in >> p.first >> p.second;
    return in;
}

void solve();

int main(){
    ios::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    solve();
    return 0;
}


void solve(){
    int a, b, k;
    cin >> a >> b >> k;
    if((a==0 || b==1)){
        if(k==0){
            cout << ("YES") << endl;
            cout << string(b, '1')+string(a, '0') << endl;
            cout << string(b, '1')+string(a, '0') << endl;
            return ;
        }
        else{
            rprintln("NO");
        }

    }
    if(k>a+b-2){
        rprintln("NO");
    }
    cout << "YES" << endl;

    string ans = "1" + string(b-1, '1') + string(a, '0');
    string base = ans;

    int lco = b-1;

    swap(ans[lco], ans[lco+min(k,a)]);
    k-=min(k,a);
    if(k==0){
        cout << base << endl;
        rprintln(ans);
    }
    swap(ans[lco], ans[lco-k]);
    cout << base << endl;
    rprintln(ans);


}

```