#include <bits/stdc++.h>
using namespace std;
const unsigned long long hash1 = 201326611;
const double eps = 1e-8;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const int inf = 0x3f3f3f3f;
const long long mod = 1e9 + 7;
const int N = 4e5 + 10;
const int M = 12;
const int dif = 26;
const double PI = acos(-1.0);
inline void Mod(long long& x) {
  if (x >= mod) x -= mod;
}
void BinaryBitset(int n) { cout << bitset<sizeof(int) * 4>(n) << endl; }
int n, k;
int a[N], b[N], f[N];
char s[N];
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) scanf("%d", &b[i]);
  int cnt = 0, ans = 0;
  for (int i = 1; i <= n; i++) {
    f[a[i]]++;
    if (f[a[i]]) cnt++;
    if (f[b[i]] == 1) cnt--;
    f[b[i]]--;
    s[a[i]] = (char)(ans + 'a');
    if (cnt == 0 && i != n) ans = min(ans + 1, k - 1);
  }
  if (ans == k - 1) {
    puts("YES");
    for (int i = 1; i <= n; i++) cout << s[i];
  } else
    puts("NO");
}

### Prompt

Please formulate a CPP solution 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;
const unsigned long long hash1 = 201326611;
const double eps = 1e-8;
const long long INF = 0x3f3f3f3f3f3f3f3f;
const int inf = 0x3f3f3f3f;
const long long mod = 1e9 + 7;
const int N = 4e5 + 10;
const int M = 12;
const int dif = 26;
const double PI = acos(-1.0);
inline void Mod(long long& x) {
  if (x >= mod) x -= mod;
}
void BinaryBitset(int n) { cout << bitset<sizeof(int) * 4>(n) << endl; }
int n, k;
int a[N], b[N], f[N];
char s[N];
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 1; i <= n; i++) scanf("%d", &b[i]);
  int cnt = 0, ans = 0;
  for (int i = 1; i <= n; i++) {
    f[a[i]]++;
    if (f[a[i]]) cnt++;
    if (f[b[i]] == 1) cnt--;
    f[b[i]]--;
    s[a[i]] = (char)(ans + 'a');
    if (cnt == 0 && i != n) ans = min(ans + 1, k - 1);
  }
  if (ans == k - 1) {
    puts("YES");
    for (int i = 1; i <= n; i++) cout << s[i];
  } else
    puts("NO");
}

```