#include <bits/stdc++.h>
using namespace std;

typedef ostringstream OSS; typedef istringstream ISS;
typedef long long LL;
typedef pair<int, int> PII;  typedef pair<LL, LL> PLL;
typedef vector<int>    VI;   typedef vector<VI>   VVI;   typedef vector<VVI>   VVVI;
typedef vector<LL>     VLL;  typedef vector<VLL>  VVLL;  typedef vector<VVLL>  VVVLL;
typedef vector<double> VD;   typedef vector<VD>   VVD;   typedef vector<VVD>   VVVD;
typedef vector<string> VS;   typedef vector<VS>   VVS;   typedef vector<VVS>   VVVS;
typedef vector<bool>   VB;   typedef vector<VB>   VVB;   typedef vector<VVB>   VVVB;
typedef vector<PII>    VPII; typedef vector<VPII> VVPII; typedef vector<VVPII> VVVPII;
typedef vector<PLL>    VPLL; typedef vector<VPLL> VVPLL; typedef vector<VVPLL> VVVPLL;

#define fst first
#define snd second
// #define Y first
// #define X second
#define MP make_pair
#define PB push_back
#define EB emplace_back 
#define ALL(x)  (x).begin(),(x).end()
#define RALL(x) (x).rbegin(),(x).rend()
#define RANGEBOX(x,y,maxX,maxY) (0 <= (x) && 0 <= (y) && (x) < (maxX) && (y) < (maxY))
#define RANGE(x, l, r) ((l) <= (x) && (x) <= (r))
#define rep(i, N)  for (int i = 0; i < (int)(N); i++)
#define rrep(i, N) for (int i = N - 1; i >= 0; i--)
#define REP(i, init, N)  for (int i = (init); i < (int)(N); i++)
#define RREP(i, N, last) for (int i = (init - 1); i >= last; i--)
#define MAXUD(orig, target) orig = max(orig, target)
#define MINUD(orig, target) orig = min(orig, target)
#define DUMP( x ) cerr << #x << " = " << ( x ) << endl

template < typename T > inline T fromString(const string &s) { T res; ISS iss(s); iss >> res; return res; };
template < typename T > inline string toString(const T &a)   { OSS oss; oss << a; return oss.str(); };

const int    INF  = 0x3f3f3f3f;
const LL     INFL = 0x3f3f3f3f3f3f3f3fLL;
const double DINF = 0x3f3f3f3f;
const int    DX[] = {1,  0, -1, 0};
const int    DY[] = {0, -1,  0, 1};
const double EPS  = 1e-12;
// const double PI   = acos(-1.0);
// lambda: [](T1 x)->T2{return y;}
// simple lambda: [](T x){return x;}

int main(void) {
    int N, D;
    string src;
    cin >> N >> src >> D;

    string dst(src);

    int cnt = 0;
    rep(i, N) {
        if (cnt >= D) break;
        if (src[i] == '0') {
            dst[i] = '1';
            ++cnt;
        }
    }

    rep(i, N) {
        if (cnt >= D) break;
        int j = N - i - 1;
        if (src[j] == '1') {
            dst[j] = '0';
            ++cnt;
        }
    }

    cout << dst << endl;

	return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

Problem statement

There is an unsigned $ 2 $ decimal integer $ X $ with $ N $ in digits including Leading-zeros. Output the largest non-negative integer that can be expressed in $ 2 $ base in $ N $ digits where the Hamming distance from $ X $ is $ D $.

The Hamming distance between integers expressed in $ 2 $ is the number of digits with different values ​​in a number of $ 2 $. For example, the Hamming distance between $ 000 $ and $ 110 $ is $ 2 $.

Constraint

$ 1 \ leq N \ leq 1000 $
$ 0 \ leq D \ leq N $
All inputs are non-negative integers

sample

Sample input 1


Five
00001
3


Sample output 1


11101


Sample input 2


7
0110100
Four


Sample output 2


1111111


Sample input 3


18
110001001110100100
6


Sample output 3


111111111111100100


Sample input 4


3
000
0


Sample output 4


000




input

$ N $
$ X $
$ D $

output

Output the integer of the answer on the $ 1 $ line in unsigned $ 2 $ decimal notation.

Example

Input

5
00001
3


Output

11101

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

typedef ostringstream OSS; typedef istringstream ISS;
typedef long long LL;
typedef pair<int, int> PII;  typedef pair<LL, LL> PLL;
typedef vector<int>    VI;   typedef vector<VI>   VVI;   typedef vector<VVI>   VVVI;
typedef vector<LL>     VLL;  typedef vector<VLL>  VVLL;  typedef vector<VVLL>  VVVLL;
typedef vector<double> VD;   typedef vector<VD>   VVD;   typedef vector<VVD>   VVVD;
typedef vector<string> VS;   typedef vector<VS>   VVS;   typedef vector<VVS>   VVVS;
typedef vector<bool>   VB;   typedef vector<VB>   VVB;   typedef vector<VVB>   VVVB;
typedef vector<PII>    VPII; typedef vector<VPII> VVPII; typedef vector<VVPII> VVVPII;
typedef vector<PLL>    VPLL; typedef vector<VPLL> VVPLL; typedef vector<VVPLL> VVVPLL;

#define fst first
#define snd second
// #define Y first
// #define X second
#define MP make_pair
#define PB push_back
#define EB emplace_back 
#define ALL(x)  (x).begin(),(x).end()
#define RALL(x) (x).rbegin(),(x).rend()
#define RANGEBOX(x,y,maxX,maxY) (0 <= (x) && 0 <= (y) && (x) < (maxX) && (y) < (maxY))
#define RANGE(x, l, r) ((l) <= (x) && (x) <= (r))
#define rep(i, N)  for (int i = 0; i < (int)(N); i++)
#define rrep(i, N) for (int i = N - 1; i >= 0; i--)
#define REP(i, init, N)  for (int i = (init); i < (int)(N); i++)
#define RREP(i, N, last) for (int i = (init - 1); i >= last; i--)
#define MAXUD(orig, target) orig = max(orig, target)
#define MINUD(orig, target) orig = min(orig, target)
#define DUMP( x ) cerr << #x << " = " << ( x ) << endl

template < typename T > inline T fromString(const string &s) { T res; ISS iss(s); iss >> res; return res; };
template < typename T > inline string toString(const T &a)   { OSS oss; oss << a; return oss.str(); };

const int    INF  = 0x3f3f3f3f;
const LL     INFL = 0x3f3f3f3f3f3f3f3fLL;
const double DINF = 0x3f3f3f3f;
const int    DX[] = {1,  0, -1, 0};
const int    DY[] = {0, -1,  0, 1};
const double EPS  = 1e-12;
// const double PI   = acos(-1.0);
// lambda: [](T1 x)->T2{return y;}
// simple lambda: [](T x){return x;}

int main(void) {
    int N, D;
    string src;
    cin >> N >> src >> D;

    string dst(src);

    int cnt = 0;
    rep(i, N) {
        if (cnt >= D) break;
        if (src[i] == '0') {
            dst[i] = '1';
            ++cnt;
        }
    }

    rep(i, N) {
        if (cnt >= D) break;
        int j = N - i - 1;
        if (src[j] == '1') {
            dst[j] = '0';
            ++cnt;
        }
    }

    cout << dst << endl;

	return 0;
}
```