#include <bits/stdc++.h>
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
void print(long long* a, long long n) {
  long long i;
  for (i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}
long long arrMax(long long* a, long long n) {
  long long i, max = a[0];
  for (i = 1; i < n; i++) {
    if (a[i] > max) max = a[i];
  }
  return max;
}
void print2d(long long a[][100], long long m, long long n) {
  long long i, j;
  for (i = 0; i < m; i++) {
    for (j = 0; j < n; j++) {
      cout << setw(2) << a[i][j];
    }
    cout << endl;
  }
}
void fio() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
set<long long> calculateFactor(long long n) {
  set<long long> temp;
  long long l = sqrt(n);
  for (long long i = 1; i <= l; i++) {
    if (n % i == 0) {
      temp.insert(i);
      temp.insert(n / i);
    }
  }
  return temp;
}
set<long long> setIntersection(set<long long> s1, set<long long> s2) {
  set<long long> temp;
  auto it1 = s1.begin();
  auto it2 = s2.begin();
  while (it1 != s1.end() && it2 != s2.end()) {
    if (*it1 > *it2) {
      *it2++;
    } else if (*it1 < *it2) {
      *it1++;
    } else {
      temp.insert(*it1);
      *it1++;
      *it2++;
    }
  }
  return temp;
}
int32_t main() {
  fio();
  long long n, k;
  cin >> n >> k;
  string s, a;
  cin >> s;
  a = s;
  long long i, j, flag1 = -1, flag2 = -1;
  for (i = 0; i < k; i++) {
    j = i + k;
    while (j < n) {
      a[j] = a[i];
      j += k;
    }
  }
  long long flag = 0;
  for (i = 0; i < n; i++) {
    if (a[i] < s[i]) {
      flag = 1;
      break;
    } else if (a[i] > s[i])
      break;
  }
  cout << n << endl;
  if (flag == 1) {
    if (a[k - 1] != '9') {
      j = k - 1;
      while (j < n) {
        a[j]++;
        j += k;
      }
    } else {
      long long x = k - 1;
      while (a[x] == '9') {
        j = x;
        while (j < n) {
          a[j] = '0';
          j += k;
        }
        x--;
      }
      j = x;
      while (j < n) {
        a[j]++;
        j += k;
      }
    }
  }
  cout << a;
}

### Prompt

In Cpp, your task is to solve the following problem:

You are given an integer x of n digits a_1, a_2, …, a_n, which make up its decimal notation in order from left to right.

Also, you are given a positive integer k < n.

Let's call integer b_1, b_2, …, b_m beautiful if b_i = b_{i+k} for each i, such that 1 ≤ i ≤ m - k.

You need to find the smallest beautiful integer y, such that y ≥ x. 

Input

The first line of input contains two integers n, k (2 ≤ n ≤ 200 000, 1 ≤ k < n): the number of digits in x and k.

The next line of input contains n digits a_1, a_2, …, a_n (a_1 ≠ 0, 0 ≤ a_i ≤ 9): digits of x.

Output

In the first line print one integer m: the number of digits in y.

In the next line print m digits b_1, b_2, …, b_m (b_1 ≠ 0, 0 ≤ b_i ≤ 9): digits of y.

Examples

Input


3 2
353


Output


3
353


Input


4 2
1234


Output


4
1313

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename Arg1>
void __f(const char* name, Arg1&& arg1) {
  cout << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args) {
  const char* comma = strchr(names + 1, ',');
  cout.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
void print(long long* a, long long n) {
  long long i;
  for (i = 0; i < n; i++) {
    cout << a[i] << " ";
  }
  cout << endl;
}
long long arrMax(long long* a, long long n) {
  long long i, max = a[0];
  for (i = 1; i < n; i++) {
    if (a[i] > max) max = a[i];
  }
  return max;
}
void print2d(long long a[][100], long long m, long long n) {
  long long i, j;
  for (i = 0; i < m; i++) {
    for (j = 0; j < n; j++) {
      cout << setw(2) << a[i][j];
    }
    cout << endl;
  }
}
void fio() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
set<long long> calculateFactor(long long n) {
  set<long long> temp;
  long long l = sqrt(n);
  for (long long i = 1; i <= l; i++) {
    if (n % i == 0) {
      temp.insert(i);
      temp.insert(n / i);
    }
  }
  return temp;
}
set<long long> setIntersection(set<long long> s1, set<long long> s2) {
  set<long long> temp;
  auto it1 = s1.begin();
  auto it2 = s2.begin();
  while (it1 != s1.end() && it2 != s2.end()) {
    if (*it1 > *it2) {
      *it2++;
    } else if (*it1 < *it2) {
      *it1++;
    } else {
      temp.insert(*it1);
      *it1++;
      *it2++;
    }
  }
  return temp;
}
int32_t main() {
  fio();
  long long n, k;
  cin >> n >> k;
  string s, a;
  cin >> s;
  a = s;
  long long i, j, flag1 = -1, flag2 = -1;
  for (i = 0; i < k; i++) {
    j = i + k;
    while (j < n) {
      a[j] = a[i];
      j += k;
    }
  }
  long long flag = 0;
  for (i = 0; i < n; i++) {
    if (a[i] < s[i]) {
      flag = 1;
      break;
    } else if (a[i] > s[i])
      break;
  }
  cout << n << endl;
  if (flag == 1) {
    if (a[k - 1] != '9') {
      j = k - 1;
      while (j < n) {
        a[j]++;
        j += k;
      }
    } else {
      long long x = k - 1;
      while (a[x] == '9') {
        j = x;
        while (j < n) {
          a[j] = '0';
          j += k;
        }
        x--;
      }
      j = x;
      while (j < n) {
        a[j]++;
        j += k;
      }
    }
  }
  cout << a;
}

```