Problem: F: Substring decomposition

problem

Given the two strings S and T and the integer k. Considering consecutive substrings of length k or more of T, determine if S can be constructed by concatenating them.

Where the string s = s_1 s_2 ... s_n is a contiguous substring s [l, r] = s_l s_ {l + 1} ... s_r (1 \ leq l \ leq r \ leq n) , S refers to a character string created by cutting out the l-th to r-th characters of s, and its length is r --l + 1.

Input format


S
T
k


Constraint

* S and T consist of lowercase alphabets
* 1 \ leq | S |, | T | \ leq 2 \ times 10 ^ 5
* 1 \ leq k \ leq | T |



Output format

Print `Yes` when S can be configured, and` No` on one line otherwise.

Input example 1


abracadabra
cadabra
Four


Output example 1


Yes

You can construct `abracadabra` by concatenating` abra` and `cadabra`, which are substrings of T with a length of 4 or more, which is a string equal to S.

Input example 2


abcd
zcba
1


Output example 2


No

Input example 3


abc
zcba
1


Output example 3


Yes

Input example 4


abcdefg
abcddefg
Four


Output example 4


No





Example

Input

abracadabra
cadabra
4


Output

Yes

Solution (in CPP):

Solution:
#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<functional>
#include<assert.h>
#include<numeric>
using namespace std;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
using ll = long long;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;



struct SuffixArray {
  vector< int > SA;
  const string s;

  SuffixArray(const string &str) : s(str) {
    SA.resize(s.size());
    iota(begin(SA), end(SA), 0);
    sort(begin(SA), end(SA), [&](int a, int b) {
      return s[a] == s[b] ? a > b : s[a] < s[b];
    });
    vector< int > classes(s.size()), c(s.begin(), s.end()), cnt(s.size());
    for(int len = 1; len < s.size(); len <<= 1) {
      for(int i = 0; i < s.size(); i++) {
        if(i > 0 && c[SA[i - 1]] == c[SA[i]] && SA[i - 1] + len < s.size() && c[SA[i - 1] + len / 2] == c[SA[i] + len / 2]) {
          classes[SA[i]] = classes[SA[i - 1]];
        } else {
          classes[SA[i]] = i;
        }
      }
      iota(begin(cnt), end(cnt), 0);
      copy(begin(SA), end(SA), begin(c));
      for(int i = 0; i < s.size(); i++) {
        int s1 = c[i] - len;
        if(s1 >= 0) SA[cnt[classes[s1]]++] = s1;
      }
      classes.swap(c);
    }
  }

  int operator[](int k) const {
    return SA[k];
  }

  size_t size() const {
    return s.size();
  }

  bool lt_substr(const string &t, int si = 0, int ti = 0) {
    int sn = (int) s.size(), tn = (int) t.size();
    while(si < sn && ti < tn) {
      if(s[si] < t[ti]) return true;
      if(s[si] > t[ti]) return false;
      ++si, ++ti;
    }
    return si >= sn && ti < tn;
  }

  int lower_bound(const string &t) {
    int low = -1, high = (int) SA.size();
    while(high - low > 1) {
      int mid = (low + high) / 2;
      if(lt_substr(t, SA[mid])) low = mid;
      else high = mid;
    }
    return high;
  }

  pair< int, int > lower_upper_bound(string &t) {
    int idx = lower_bound(t);
    int low = idx - 1, high = (int) SA.size();
    t.back()++;
    while(high - low > 1) {
      int mid = (low + high) / 2;
      if(lt_substr(t, SA[mid])) low = mid;
      else high = mid;
    }
    t.back()--;
    return {idx, high};
  }

  void output() {
    for(int i = 0; i < size(); i++) {
      cout << i << ": " << s.substr(SA[i]) << endl;
    }
  }
};


struct LongestCommonPrefixArray {
  const SuffixArray &SA;
  vector< int > LCP, rank;

  LongestCommonPrefixArray(const SuffixArray &SA) : SA(SA), LCP(SA.size()) {
    rank.resize(SA.size());
    for(int i = 0; i < SA.size(); i++) {
      rank[SA[i]] = i;
    }
    for(int i = 0, h = 0; i < SA.size(); i++) {
      if(rank[i] + 1 < SA.size()) {
        for(int j = SA[rank[i] + 1]; max(i, j) + h < SA.size() && SA.s[i + h] == SA.s[j + h]; ++h);
        LCP[rank[i] + 1] = h;
        if(h > 0) --h;
      }
    }
  }

  int operator[](int k) const {
    return LCP[k];
  }

  size_t size() const {
    return LCP.size();
  }

  void output() {
    for(int i = 0; i < size(); i++) {
      cout << i << ": " << LCP[i] << " " << SA.s.substr(SA[i]) << endl;
    }
  }
};

template<typename T, typename S>
struct LazySegmentTree{
private:
    int n;
    vector<T> node;
    vector<S> lazy;
    T E0;
    S E1;

    inline void updatef(S& lazy,S& value){
        //lazy += value;
        lazy = value;
        //lazy = max(lazy, value);
        //lazy = min(lazy, value);
    }
    inline void calculatef(T& node,S& lazy,int len){
        //node += lazy * len; //区間sumはこっち
        node += lazy ; //区間maxとか
        //node = lazy ;
    }
    inline T queryf(T& x,T& y){
        //return x + y;
        //return x * y;
        return max(x, y);
        //return min(x, y);
    }
public:
    LazySegmentTree(int sz,T nodeE,S lazyE ):E0(nodeE), E1(lazyE){
        n=1;
        while(n<sz)n<<=1;
        node.resize(2*n-1,E0);
        lazy.resize(2*n-1,E1);
    }

    LazySegmentTree(vector<T>& v,T E0,S E1 ):E0(E0),E1(E1){
        n=1;
        int sz=v.size();
        while(n<sz)n<<=1;
        node.resize(2*n-1,E0);
        lazy.resize(2*n-1,E1);
        rep(i,sz)node[i+n-1] = v[i];
        for(int i=n-2; i>=0; --i){
            node[i] = queryf(node[2*i+1],node[2*i+2]);
        }
    }

    void eval(int k,int l,int r){
        if(lazy[k]==E1)return ;
        calculatef(node[k], lazy[k], r-l);
        if(r-l>1){
            updatef(lazy[2*k+1], lazy[k]);
            updatef(lazy[2*k+2], lazy[k]);
        }
        lazy[k]=E1;
    }

    void update(int a, int b, S x,int k=0,int l=0,int r=-1){
        if(r<0)r=n;
        eval(k,l,r);
        if(r<=a||b<=l)return;
        if(a<=l&&r<=b){
            updatef(lazy[k], x);
            eval(k,l,r);
        }
        else {
            update(a,b,x,2*k+1,l,(l+r)/2);
            update(a,b,x,2*k+2,(l+r)/2,r);
            node[k]=queryf(node[2*k+1], node[2*k+2]);
        }
    }

    T query(int a,int b,int k=0,int l=0,int r=-1){
        if(r<0)r=n;
        eval(k,l,r);
        if(r<=a||b<=l)return E0;
        if(a<=l&&r<=b)return node[k];
        T xl=query(a,b,2*k+1,l,(l+r)/2);
        T xr=query(a,b,2*k+2,(l+r)/2,r);
        return queryf(xl, xr);
    }
};
int main(){
    string s, t;
    cin>>s>>t;
    int k;
    cin>>k;
    string u = s+"$"+t;
    SuffixArray sa(u);
    LongestCommonPrefixArray lcp(sa);
    int m = u.size();
    int n = s.size();
    vector<int> res(m);
    int ma = 0;
    rep(i,m){
        if(lcp.SA[i]>n)ma = inf;
        else {
            ma = min(ma,lcp.LCP[i]);
            res[lcp.SA[i]]=max(res[lcp.SA[i]],ma);
        }
    }
    ma = 0;
    for(int i=m-1;i>=0;--i){
        if(lcp.SA[i]>n)ma = lcp.LCP[i];
        else {
            res[lcp.SA[i]]=max(res[lcp.SA[i]],ma);
            ma = min(ma,lcp.LCP[i]);
        }

    }
    LazySegmentTree<int,int> sg(n+5,0,0);
    sg.update(0,1,1);
    rep(i,n){
        if(res[i]<k)continue;
        auto ret = sg.query(i,i+1);
        if(ret)sg.update(i+k,i+res[i]+1,1);
    }
    cout<<(sg.query(n,n+1)?"Yes":"No")<<endl;
    return 0;
}