#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int mod = (ll)1e9 + 7;
const int INF = 1e9 + 1;
const int N = 2e5 + 100;
const double eps = 1e-3;
template <typename XPAX>
void ckma(XPAX &x, XPAX y) {
  x = (x < y ? y : x);
}
template <typename XPAX>
void ckmi(XPAX &x, XPAX y) {
  x = (x > y ? y : x);
}
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void solve() {
  int n;
  cin >> n;
  int k;
  cin >> k;
  string s;
  cin >> s;
  auto is_greater = [&](string t) {
    if (t.size() > s.size()) return 1;
    for (int i = 0; i < (n); ++i) {
      if (t[i] > s[i])
        return 1;
      else if (s[i] > t[i])
        return 0;
    }
    return 1;
  };
  string t = "";
  for (int i = 0; i < (n); ++i) {
    if (i < k)
      t += s[i];
    else
      t += t[i - k];
  }
  cerr << "["
       << "t"
       << "] = [";
  _print(t);
  if (is_greater(t)) {
    cout << t.size() << '\n';
    cout << t << '\n';
    return;
  }
  int id = -1;
  for (int i = 0; i < (k); ++i) {
    if (t[i] != '9') id = i;
  }
  if (id != -1) {
    cerr << "["
         << "id"
         << "] = [";
    _print(id);
    int p = t[id] - '0';
    ++p;
    char c = char('0' + p);
    for (int j = id; j < n; j += k) {
      t[j] = c;
    }
    for (int i = id + 1; i < k; ++i) {
      if (t[i] == '9') {
        for (int j = i; j < n; j += k) {
          t[j] = '0';
        }
      }
    }
  } else {
    t = string('0', n);
    t = '1' + t;
  }
  cout << t.size() << '\n';
  cout << t << '\n';
}
void test_case() {
  int t;
  cin >> t;
  for (int p = 0; p < (t); ++p) {
    solve();
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  solve();
}

### 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;
using ll = long long;
int mod = (ll)1e9 + 7;
const int INF = 1e9 + 1;
const int N = 2e5 + 100;
const double eps = 1e-3;
template <typename XPAX>
void ckma(XPAX &x, XPAX y) {
  x = (x < y ? y : x);
}
template <typename XPAX>
void ckmi(XPAX &x, XPAX y) {
  x = (x > y ? y : x);
}
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V> &x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T &x) {
  int f = 0;
  cerr << '{';
  for (auto &i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void solve() {
  int n;
  cin >> n;
  int k;
  cin >> k;
  string s;
  cin >> s;
  auto is_greater = [&](string t) {
    if (t.size() > s.size()) return 1;
    for (int i = 0; i < (n); ++i) {
      if (t[i] > s[i])
        return 1;
      else if (s[i] > t[i])
        return 0;
    }
    return 1;
  };
  string t = "";
  for (int i = 0; i < (n); ++i) {
    if (i < k)
      t += s[i];
    else
      t += t[i - k];
  }
  cerr << "["
       << "t"
       << "] = [";
  _print(t);
  if (is_greater(t)) {
    cout << t.size() << '\n';
    cout << t << '\n';
    return;
  }
  int id = -1;
  for (int i = 0; i < (k); ++i) {
    if (t[i] != '9') id = i;
  }
  if (id != -1) {
    cerr << "["
         << "id"
         << "] = [";
    _print(id);
    int p = t[id] - '0';
    ++p;
    char c = char('0' + p);
    for (int j = id; j < n; j += k) {
      t[j] = c;
    }
    for (int i = id + 1; i < k; ++i) {
      if (t[i] == '9') {
        for (int j = i; j < n; j += k) {
          t[j] = '0';
        }
      }
    }
  } else {
    t = string('0', n);
    t = '1' + t;
  }
  cout << t.size() << '\n';
  cout << t << '\n';
}
void test_case() {
  int t;
  cin >> t;
  for (int p = 0; p < (t); ++p) {
    solve();
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  solve();
}

```