#include <bits/stdc++.h>
using namespace std;
bool comp(pair<long long, char> aa, pair<long long, char> bb) {
  if (aa.first != bb.first) return aa.first > bb.first;
  return aa.second < bb.second;
}
bool comp1(pair<long long, char> aa, pair<long long, char> bb) {
  if (aa.first != bb.first) return aa.first < bb.first;
  return aa.second > bb.second;
}
bool comp2(pair<long long, long long> aa, pair<long long, long long> bb) {
  if (aa.first != bb.first) return aa.first > bb.first;
  return aa.second < bb.second;
}
bool comp3(pair<long long, long long> aa, pair<long long, long long> bb) {
  if (aa.first != bb.first) return aa.first < bb.first;
  return aa.second > bb.second;
}
long long rup(long long ik, long long ikk) {
  if (ik % ikk == 0)
    return ik / ikk;
  else
    return (ik / ikk) + 1;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long modpow(long long x, long long n, long long m) {
  if (n == 0) return 1 % m;
  long long u = modpow(x, n / 2, m);
  u = (u * u) % m;
  if (n % 2 == 1) u = (u * x) % m;
  return u;
}
long long nm(long long a, long long b) { return (b + (a % b)) % b; }
struct hash_pair {
  template <class T1, class T2>
  size_t operator()(const pair<T1, T2>& p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};
string findSum(string str1, string str2) {
  if (str1.length() > str2.length()) swap(str1, str2);
  string str = "";
  long long n1 = str1.length(), n2 = str2.length();
  reverse(str1.begin(), str1.end());
  reverse(str2.begin(), str2.end());
  long long carry = 0;
  for (long long i = 0; i < n1; i++) {
    long long sum = ((str1[i] - '0') + (str2[i] - '0') + carry);
    str.push_back(sum % 10 + '0');
    carry = sum / 10;
  }
  for (long long i = n1; i < n2; i++) {
    long long sum = ((str2[i] - '0') + carry);
    str.push_back(sum % 10 + '0');
    carry = sum / 10;
  }
  if (carry) str.push_back(carry + '0');
  reverse(str.begin(), str.end());
  return str;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    long long j;
    string xx = "";
    for (j = 0; j <= k - 1; j = j + 1) {
      xx += s[j];
    }
    string yy = findSum("1", xx);
    long long pp = n / k;
    long long qq = n % k;
    string ans = "";
    string ans2 = "";
    for (j = 1; j <= pp; j = j + 1) {
      ans += xx;
    }
    for (j = 0; j <= qq - 1; j = j + 1) {
      ans += xx[j];
    }
    long long k2 = yy.length();
    if (k2 > k) n++;
    pp = n / k2;
    qq = n % k2;
    for (j = 1; j <= pp; j = j + 1) {
      ans2 += yy;
    }
    for (j = 0; j <= qq - 1; j = j + 1) {
      ans2 += yy[j];
    }
    if (ans >= s) {
      cout << ans.length() << "\n";
      cout << ans << "\n";
    } else {
      cout << ans2.length() << "\n";
      cout << ans2 << "\n";
    }
  }
}

### Prompt

Generate 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;
bool comp(pair<long long, char> aa, pair<long long, char> bb) {
  if (aa.first != bb.first) return aa.first > bb.first;
  return aa.second < bb.second;
}
bool comp1(pair<long long, char> aa, pair<long long, char> bb) {
  if (aa.first != bb.first) return aa.first < bb.first;
  return aa.second > bb.second;
}
bool comp2(pair<long long, long long> aa, pair<long long, long long> bb) {
  if (aa.first != bb.first) return aa.first > bb.first;
  return aa.second < bb.second;
}
bool comp3(pair<long long, long long> aa, pair<long long, long long> bb) {
  if (aa.first != bb.first) return aa.first < bb.first;
  return aa.second > bb.second;
}
long long rup(long long ik, long long ikk) {
  if (ik % ikk == 0)
    return ik / ikk;
  else
    return (ik / ikk) + 1;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long modpow(long long x, long long n, long long m) {
  if (n == 0) return 1 % m;
  long long u = modpow(x, n / 2, m);
  u = (u * u) % m;
  if (n % 2 == 1) u = (u * x) % m;
  return u;
}
long long nm(long long a, long long b) { return (b + (a % b)) % b; }
struct hash_pair {
  template <class T1, class T2>
  size_t operator()(const pair<T1, T2>& p) const {
    auto hash1 = hash<T1>{}(p.first);
    auto hash2 = hash<T2>{}(p.second);
    return hash1 ^ hash2;
  }
};
string findSum(string str1, string str2) {
  if (str1.length() > str2.length()) swap(str1, str2);
  string str = "";
  long long n1 = str1.length(), n2 = str2.length();
  reverse(str1.begin(), str1.end());
  reverse(str2.begin(), str2.end());
  long long carry = 0;
  for (long long i = 0; i < n1; i++) {
    long long sum = ((str1[i] - '0') + (str2[i] - '0') + carry);
    str.push_back(sum % 10 + '0');
    carry = sum / 10;
  }
  for (long long i = n1; i < n2; i++) {
    long long sum = ((str2[i] - '0') + carry);
    str.push_back(sum % 10 + '0');
    carry = sum / 10;
  }
  if (carry) str.push_back(carry + '0');
  reverse(str.begin(), str.end());
  return str;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  while (t--) {
    long long n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    long long j;
    string xx = "";
    for (j = 0; j <= k - 1; j = j + 1) {
      xx += s[j];
    }
    string yy = findSum("1", xx);
    long long pp = n / k;
    long long qq = n % k;
    string ans = "";
    string ans2 = "";
    for (j = 1; j <= pp; j = j + 1) {
      ans += xx;
    }
    for (j = 0; j <= qq - 1; j = j + 1) {
      ans += xx[j];
    }
    long long k2 = yy.length();
    if (k2 > k) n++;
    pp = n / k2;
    qq = n % k2;
    for (j = 1; j <= pp; j = j + 1) {
      ans2 += yy;
    }
    for (j = 0; j <= qq - 1; j = j + 1) {
      ans2 += yy[j];
    }
    if (ans >= s) {
      cout << ans.length() << "\n";
      cout << ans << "\n";
    } else {
      cout << ans2.length() << "\n";
      cout << ans2 << "\n";
    }
  }
}

```