#include <bits/stdc++.h>
using namespace std;
template <class R>
inline void Readin(R &K) {
  bool F = K = 0;
  char C = getchar();
  while (C < '0' || C > '9') {
    if (C == '-') F = 1;
    C = getchar();
  }
  while (C <= '9' && C >= '0') K = (K << 1) + (K << 3) + C - '0', C = getchar();
  if (F) K = -K;
}
template <class R>
inline bool Checkmax(R &A, R B) {
  return A < B ? A = B, 1 : 0;
}
template <class R>
inline bool Checkmin(R &A, R B) {
  return A > B ? A = B, 1 : 0;
}
const int MaxN = 200000 + 10;
int N, K;
int P[MaxN], Q[MaxN], Inv[MaxN], Cnt;
char Ans[MaxN];
int main() {
  Readin(N);
  Readin(K);
  for (register int i = 0; ++i <= N;) {
    Readin(P[i]);
    Inv[P[i]] = i;
  }
  for (register int i = 0; ++i <= N;) {
    register int X;
    Readin(X);
    Q[i] = Inv[X];
  }
  for (register int i = 0, Now = 0, Last = 0; ++i <= N;) {
    Checkmax(Now, Q[i]);
    if (Now == i) {
      ++Cnt;
      for (register int i = Last; ++i <= Now;)
        Ans[P[i]] = 'a' + min(Cnt, 26) - 1;
      Last = Now;
    }
  }
  if (Cnt < K) return not printf("NO\n");
  printf("YES\n");
  for (register int i = 0; ++i <= N;) {
    putchar(Ans[i]);
  }
  return not printf("\n");
}

### Prompt

Please create a solution in Cpp to the following problem:

Authors have come up with the string s consisting of n lowercase Latin letters.

You are given two permutations of its indices (not necessary equal) p and q (both of length n). Recall that the permutation is the array of length n which contains each integer from 1 to n exactly once.

For all i from 1 to n-1 the following properties hold: s[p_i] ≤ s[p_{i + 1}] and s[q_i] ≤ s[q_{i + 1}]. It means that if you will write down all characters of s in order of permutation indices, the resulting string will be sorted in the non-decreasing order.

Your task is to restore any such string s of length n consisting of at least k distinct lowercase Latin letters which suits the given permutations.

If there are multiple answers, you can print any of them.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 26) — the length of the string and the number of distinct characters required.

The second line of the input contains n integers p_1, p_2, ..., p_n (1 ≤ p_i ≤ n, all p_i are distinct integers from 1 to n) — the permutation p.

The third line of the input contains n integers q_1, q_2, ..., q_n (1 ≤ q_i ≤ n, all q_i are distinct integers from 1 to n) — the permutation q.

Output

If it is impossible to find the suitable string, print "NO" on the first line.

Otherwise print "YES" on the first line and string s on the second line. It should consist of n lowercase Latin letters, contain at least k distinct characters and suit the given permutations.

If there are multiple answers, you can print any of them.

Example

Input


3 2
1 2 3
1 3 2


Output


YES
abb

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class R>
inline void Readin(R &K) {
  bool F = K = 0;
  char C = getchar();
  while (C < '0' || C > '9') {
    if (C == '-') F = 1;
    C = getchar();
  }
  while (C <= '9' && C >= '0') K = (K << 1) + (K << 3) + C - '0', C = getchar();
  if (F) K = -K;
}
template <class R>
inline bool Checkmax(R &A, R B) {
  return A < B ? A = B, 1 : 0;
}
template <class R>
inline bool Checkmin(R &A, R B) {
  return A > B ? A = B, 1 : 0;
}
const int MaxN = 200000 + 10;
int N, K;
int P[MaxN], Q[MaxN], Inv[MaxN], Cnt;
char Ans[MaxN];
int main() {
  Readin(N);
  Readin(K);
  for (register int i = 0; ++i <= N;) {
    Readin(P[i]);
    Inv[P[i]] = i;
  }
  for (register int i = 0; ++i <= N;) {
    register int X;
    Readin(X);
    Q[i] = Inv[X];
  }
  for (register int i = 0, Now = 0, Last = 0; ++i <= N;) {
    Checkmax(Now, Q[i]);
    if (Now == i) {
      ++Cnt;
      for (register int i = Last; ++i <= Now;)
        Ans[P[i]] = 'a' + min(Cnt, 26) - 1;
      Last = Now;
    }
  }
  if (Cnt < K) return not printf("NO\n");
  printf("YES\n");
  for (register int i = 0; ++i <= N;) {
    putchar(Ans[i]);
  }
  return not printf("\n");
}

```