#include <bits/stdc++.h>
using namespace std;
int a[200005], b[200005];
vector<int> adj[200005], rev[200005], grafo[200005];
vector<int> idGroup[200005];
char res[200005], last;
void topo(int u, int *vis, stack<int> &topp) {
  vis[u] = 1;
  for (int v : adj[u]) {
    if (!vis[v]) topo(v, vis, topp);
  }
  topp.push(u);
}
void solve(int u, int *vis, vector<int> &cmp) {
  vis[u] = 1;
  cmp.push_back(u);
  for (int v : rev[u]) {
    if (!vis[v]) solve(v, vis, cmp);
  }
}
void go(int u, int *vis) {
  vis[u] = 1;
  last = min((char)(last + 1), 'z');
  for (int v : idGroup[u]) res[v] = last;
  for (int v : grafo[u])
    if (u != v) go(v, vis);
}
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < n; i++) scanf("%d", &b[i]);
  for (int i = 0; i < n - 1; i++) {
    adj[a[i]].push_back(a[i + 1]);
    rev[a[i + 1]].push_back(a[i]);
  }
  for (int i = 0; i < n - 1; i++) {
    adj[b[i]].push_back(b[i + 1]);
    rev[b[i + 1]].push_back(b[i]);
  }
  stack<int> topp;
  int vis[200005];
  memset(vis, 0, sizeof vis);
  for (int i = 1; i <= n; i++)
    if (!vis[i]) topo(i, vis, topp);
  memset(vis, 0, sizeof vis);
  int cnt = 0;
  vector<int> nodes;
  while (!topp.empty()) {
    int u = topp.top();
    topp.pop();
    if (!vis[u]) {
      cnt++;
      vector<int> comp;
      solve(u, vis, comp);
      sort(comp.begin(), comp.end());
      set<int> fwd, backwd;
      for (int u : comp) {
        for (int v : adj[u])
          if (!binary_search(comp.begin(), comp.end(), v)) fwd.insert(v);
        for (int v : rev[u])
          if (!binary_search(comp.begin(), comp.end(), v)) backwd.insert(v);
      }
      for (int v : backwd) grafo[v].push_back(comp[0]);
      for (int v : comp) idGroup[comp[0]].push_back(v);
      nodes.push_back(comp[0]);
    }
  }
  if (cnt < k) {
    cout << "NO" << endl;
    return 0;
  }
  memset(vis, 0, sizeof vis);
  last = 'a' - 1;
  for (int x : nodes)
    if (!vis[x]) go(x, vis);
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) cout << res[i];
  cout << endl;
  return 0;
}

### Prompt

Your task is to create 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;
int a[200005], b[200005];
vector<int> adj[200005], rev[200005], grafo[200005];
vector<int> idGroup[200005];
char res[200005], last;
void topo(int u, int *vis, stack<int> &topp) {
  vis[u] = 1;
  for (int v : adj[u]) {
    if (!vis[v]) topo(v, vis, topp);
  }
  topp.push(u);
}
void solve(int u, int *vis, vector<int> &cmp) {
  vis[u] = 1;
  cmp.push_back(u);
  for (int v : rev[u]) {
    if (!vis[v]) solve(v, vis, cmp);
  }
}
void go(int u, int *vis) {
  vis[u] = 1;
  last = min((char)(last + 1), 'z');
  for (int v : idGroup[u]) res[v] = last;
  for (int v : grafo[u])
    if (u != v) go(v, vis);
}
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  for (int i = 0; i < n; i++) scanf("%d", &b[i]);
  for (int i = 0; i < n - 1; i++) {
    adj[a[i]].push_back(a[i + 1]);
    rev[a[i + 1]].push_back(a[i]);
  }
  for (int i = 0; i < n - 1; i++) {
    adj[b[i]].push_back(b[i + 1]);
    rev[b[i + 1]].push_back(b[i]);
  }
  stack<int> topp;
  int vis[200005];
  memset(vis, 0, sizeof vis);
  for (int i = 1; i <= n; i++)
    if (!vis[i]) topo(i, vis, topp);
  memset(vis, 0, sizeof vis);
  int cnt = 0;
  vector<int> nodes;
  while (!topp.empty()) {
    int u = topp.top();
    topp.pop();
    if (!vis[u]) {
      cnt++;
      vector<int> comp;
      solve(u, vis, comp);
      sort(comp.begin(), comp.end());
      set<int> fwd, backwd;
      for (int u : comp) {
        for (int v : adj[u])
          if (!binary_search(comp.begin(), comp.end(), v)) fwd.insert(v);
        for (int v : rev[u])
          if (!binary_search(comp.begin(), comp.end(), v)) backwd.insert(v);
      }
      for (int v : backwd) grafo[v].push_back(comp[0]);
      for (int v : comp) idGroup[comp[0]].push_back(v);
      nodes.push_back(comp[0]);
    }
  }
  if (cnt < k) {
    cout << "NO" << endl;
    return 0;
  }
  memset(vis, 0, sizeof vis);
  last = 'a' - 1;
  for (int x : nodes)
    if (!vis[x]) go(x, vis);
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) cout << res[i];
  cout << endl;
  return 0;
}

```