#include <bits/stdc++.h>
using namespace std;
const int N = int(1e4 + 5);
const int INF = int(1e9);
const int MOD = int(1e9 + 9);
bool cmp(deque<char> x, deque<char> y) {
  if (x.size() > y.size()) return true;
  if (x.size() < y.size()) return false;
  for (int i = 0; i < x.size(); i++) {
    if (x[i] > y[i]) return true;
    if (x[i] < y[i]) return false;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  deque<char> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  deque<char> b, c;
  for (int i = 0; i < k; i++) {
    b.emplace_back(a[i]);
    c.emplace_back(a[i]);
  }
  while (b.size() < a.size()) {
    b.push_back(b[b.size() - k]);
  }
  if (cmp(b, a)) {
    cout << b.size() << '\n';
    for (auto i : b) cout << i;
    return 0;
  }
  int r = c.size() - 1;
  while (r >= 0 && c[r] == '9') {
    c[r] = '0';
    r--;
  }
  if (r == -1)
    c.push_front('1');
  else
    c[r]++;
  while (c.size() < a.size()) {
    c.push_back(c[c.size() - k]);
  }
  cout << c.size() << '\n';
  for (auto i : c) cout << i;
  return 0;
}

### Prompt

Please formulate a CPP solution to 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;
const int N = int(1e4 + 5);
const int INF = int(1e9);
const int MOD = int(1e9 + 9);
bool cmp(deque<char> x, deque<char> y) {
  if (x.size() > y.size()) return true;
  if (x.size() < y.size()) return false;
  for (int i = 0; i < x.size(); i++) {
    if (x[i] > y[i]) return true;
    if (x[i] < y[i]) return false;
  }
  return true;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  deque<char> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  deque<char> b, c;
  for (int i = 0; i < k; i++) {
    b.emplace_back(a[i]);
    c.emplace_back(a[i]);
  }
  while (b.size() < a.size()) {
    b.push_back(b[b.size() - k]);
  }
  if (cmp(b, a)) {
    cout << b.size() << '\n';
    for (auto i : b) cout << i;
    return 0;
  }
  int r = c.size() - 1;
  while (r >= 0 && c[r] == '9') {
    c[r] = '0';
    r--;
  }
  if (r == -1)
    c.push_front('1');
  else
    c[r]++;
  while (c.size() < a.size()) {
    c.push_back(c[c.size() - k]);
  }
  cout << c.size() << '\n';
  for (auto i : c) cout << i;
  return 0;
}

```