#include <bits/stdc++.h>
using namespace std;

// --------------------------------------------------------------------------------------------------------------

//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

namespace VvyLw {
namespace Twitter {
void wa_haya_exe(){ cin.tie(nullptr); ios::sync_with_stdio(false); }
}
void solve();
}; // VvyLw

mt19937 EhaL(hash<string>()("Huitloxopetl"));
mt19937 Random() {
    random_device seed_gen;
    mt19937 engine {seed_gen()};
    return engine;
}

// --------------------------------------------------------------------------------------------------------------

#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0; i<n; ++i)
#define rep2(i,n) for(ll i=0; i<n; ++i)
#define rep3(i,a,b) for(ll i=a; i<=b; ++i)
#define rep4(i,a,b,c) for(ll i=a; i<=b; i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rvp1(n) for(ll i=n-1; i>=0; i--)
#define rvp2(i,n) for(ll i=n-1; i>=0; i--)
#define rvp3(i,a,b) for(ll i=a; i>=b; i--)
#define rvp4(i,a,b,c) for(ll i=a; i>=b; i-=c)
#define rvp(...) overload4(__VA_ARGS__,rvp4,rvp3,rvp2,rvp1)(__VA_ARGS__)
#define all1(v) v.begin(),v.end()
#define all2(v,a) v.begin(),v.begin()+a
#define all3(v,a,b) v.begin()+a,v.begin()+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(v) v.rbegin(),v.rend()
#define rall2(v,a) v.rbegin(),v.rbegin()+a
#define rall3(v,a,b) v.rbegin()+a,v.rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define each1(elem,v) for(auto &elem: v)
#define each2(x,y,v) for(auto &[x,y]: v)
#define each3(x,y,z,v) for(auto &[x,y,z]: v)
#define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__)
#define sqrp1(n) for(ll i=0; i*i<n; ++i)
#define sqrp2(i,n) for(ll i=0; i*i<n; ++i)
#define sqrp3(i,a,b) for(ll i=a; i*i<=b; ++i)
#define sqrp(...) overload3(__VA_ARGS__,sqrp3,sqrp2,sqrp1)(__VA_ARGS__)
#define irp(it,v) for(auto it=v.begin(); it!=v.end(); ++it)
#define ir(it,v) for(auto it=v.begin(); it!=v.end();)
#define FE(v,f) for_each(all(v),f)

using ll = long long;
using ld = long double;
using uint = unsigned;
using ul = unsigned long long;
namespace vectors {
template <class T> using V = vector<T>;
using vi = V<ll>;
using vu = V<ul>;
using vd = V<ld>;
using vc = V<char>;
using vs = V<string>;
using vb = V<bool>;
using wi = V<vi>;
using wu = V<vu>;
using wd = V<vd>;
using wc = V<vc>;
using ws = V<vs>;
using wb = V<vb>;
template <class T> V<T>& operator++(V<T>& v) { each(el,v) el++; return v; }
template <class T> V<T>& operator--(V<T>& v) { each(el,v) el--; return v; }
template <class T, class U> V<T>& operator+=(V<T>& v, const U x) { each(el,v) el+=x; return v; }
template <class T, class U> V<T>& operator-=(V<T>& v, const U x) { each(el,v) el-=x; return v; }
template <class T, class U> V<T>& operator*=(V<T>& v, const U x) { each(el,v) el*=x; return v; }
template <class T, class U> V<T>& operator/=(V<T>& v, const U x) { each(el,v) el/=x; return v; }
template <class T, class U> V<T> operator+(const V<T>& v, const U x) { V<T> res = v; res+=x; return res; }
template <class T, class U> V<T> operator-(const V<T>& v, const U x) { V<T> res = v; res-=x; return res; }
template <class T, class U> V<T> operator*(const V<T>& v, const U x) { V<T> res = v; res*=x; return res; }
template <class T, class U> V<T> operator/(const V<T>& v, const U x) { V<T> res = v; res/=x; return res; }
template <class T, class U> bool operator==(const V<T>& v, const V<T>& w) { return (v.size()==w.size() && equal(all(v),w.begin())); }
template <class T, class U> bool operator!=(const V<T>& v, const V<T>& w) { return !(v==w); }
} // vectors
using namespace vectors;
namespace pairs {
template <class T, class U> using P = pair<T, U>;
template <class T> using PP = P<T,T>;
using pi = PP<ll>;
using pd = PP<ld>;
using pc = PP<char>;
using ps = PP<string>;
template <class T> PP<T> operator+(const PP<T>& a, const PP<T>& b) { return {a.first + b.first, a.second + b.second}; }
template <class T> PP<T> operator-(const PP<T>& a, const PP<T>& b) { return {a.first - b.first, a.second - b.second}; }
template <class T> PP<T> operator-(const PP<T>& a) { return {-a.first, -a.second}; }
template <class T, class U> PP<T> operator*(const PP<T>& a, const U& b) { return {a.first * b, a.second * b}; }
template <class T, class U> PP<T> operator/(const PP<T>& a, const U& b) { return {a.first / b, a.second / b}; }
template <class T> PP<T>& operator+=(PP<T>& a, const PP<T>& b) { return a = a + b; }
template <class T> PP<T>& operator-=(PP<T>& a, const PP<T>& b) { return a = a - b; }
template <class T, class U> PP<T>& operator*=(PP<T>& a, const U& b) { return a = a * b; }
template <class T, class U> PP<T>& operator/=(PP<T>& a, const U& b) { return a = a / b; }
template <class T> bool operator==(const PP<T> &p, const PP<T> &q){ return p.first==q.first && p.second==q.second; }
template <class T> bool operator!=(const PP<T> &p, const PP<T> &q){ return !(p==q); }
template <class T, class U> bool operator==(const P<T,U> &p, const P<T,U> &q){ return p.first==q.first && p.second==q.second; }
template <class T, class U> bool operator!=(const P<T,U> &p, const P<T,U> &q){ return !(p==q); }
template <class T> PP<T> rotate(const PP<T>& a) { return {-a.second, a.first}; } // 90 degree ccw
template <class T> T dot(const PP<T>& a, const PP<T>& b) { return a.first * b.first + a.second * b.second; }
template <class T> T cross(const PP<T>& a, const PP<T>& b) { return dot(rotate(a), b); }
template <class T> T square(const PP<T>& a) { return dot(a, a); }
template <class T> ld abs(const PP<T>& a) { return hypotl(a.first, a.second); }
template <class T> T gcd(const PP<T>& a) { return gcd(a.first, a.second); }
template <class T> PP<T> normalize(PP<T> a) {
    if(a == PP<T>{}) return a;
    a /= gcd(a);
    if(a < PP<T>{}) a = -a;
    return a;
}
template <class T, class U> P<U,T> swap(P<T,U> &p){ P<U,T> ret={p.second,p.first}; return ret; }
template <class T, class U> V<P<U,T>> swap(V<P<T,U>> &vp) {
    V<P<U,T>> ret;
    FE(vp,[&ret](P<T,U> el){ret.emplace_back(pairs::swap(el));});
    return ret;
}
template <class T, class U> V<T> first(const V<P<T,U>> &vp) {
    V<T> res;
    each(el,vp) res.emplace_back(el.first);
    return res;
}
template <class T, class U> V<U> second(const V<P<T,U>> &vp) {
    V<U> res;
    each(el,vp) res.emplace_back(el.second);
    return res;
}
} // pairs
using namespace pairs;
template <class T> using pq = priority_queue<T>;
template <class T> using pqr = priority_queue<T,V<T>,greater<T>>;
template <class T, class U> using pqs = priority_queue<P<T,U>>;
template <class T, class U> using pqrs = priority_queue<P<T,U>,V<P<T,U>>,greater<P<T,U>>>;
template <class T, class U> bool chmax(T& a, const U& b) { if (a<b) { a=b; return 1; } return 0; }
template <class T, class U> bool chmin(T& a, const U& b) { if (a>b) { a=b; return 1; } return 0; }
template <class T, class U> inline bool overflow_if_add(T a, U b) { return (numeric_limits<T>::max()-a)<b; }
template <class T, class U> inline bool overflow_if_mul(T a, U b) { return (numeric_limits<T>::max()/a)<b; }
const int dx[]={0,0,-1,1,-1,-1,1,1};
const int dy[]={-1,1,0,0,-1,1,-1,1};
const int MOD = 998244353;
const int M0D = 1000000007;
const int INF = 0x3fffffff;
const ll LINF = 0x1fffffffffffffff;
const ld DINF = numeric_limits<ld>::infinity();
const double PI = acos(-1);
const double E = 2.718281828459045;

namespace IO {
template <class T> void scan(T& a){ cin >> a; }
template <class T, class U> void scan(P<T,U>& p){ scan(p.first); scan(p.second); }
template <class T> void scan(V<T>& a){ each(i,a) scan(i); }
template <class T> void lin(T& a){ getline(cin, a); }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
template <class T> void print(const T& a){ cout << a; }
template <class T> void println(const T& a){ cout << a; }
template <class T, class U> void print(const P<T,U>& p){ print(p.first); cout<<" "; print(p.second); }
template <class T> void print(const V<T>& a){ if(!a.empty()){ print(a[0]); for(auto i=a.begin(); ++i!=a.end();){ cout<<' '; print(*i); } } }
template <class T> void println(const V<T>& a){ if(!a.empty()){ print(a[0]); for(auto i=a.begin(); ++i!=a.end();){ cout<<'\n'; print(*i); } } }
template <class T, class U> void print(const map<T,U> &m){ if(!m.empty()){ print(m.begin()->first); cout<<' '; print(m.begin()->second); for(auto i=m.begin(); ++i!=m.end();){ cout<<", "; print(i->first); cout<<' '; print(i->second); } } }
template <class T> void print(const set<T> &st){ print(*st.begin()); for(auto i=st.begin(); ++i!=st.end();){ cout<<' '; print(*i); } }
template <class T> void print(queue<T> que){ print(que.front()); while(que.size()){ cout<<' '; que.pop(); if(!que.empty()) print(que.front()); } }
template <class T> void print(deque<T> dq){ print(dq.front()); while(dq.size()){ cout<<' '; dq.pop_front(); if(!dq.empty()) print(dq.front()); } }
template <class T> void print(stack<T> sk){ print(sk.top()); while(sk.size()){ cout<<' '; sk.pop(); if(!sk.empty()) print(sk.top()); } }
template <class T, class Container, class Compare> void print(priority_queue<T, Container, Compare> pq){ print(pq.top()); while(pq.size()){ pq.pop(); cout<<' '; if(!pq.empty()) print(pq.top()); } }
void bl(){ cout<<' '; }
void out(){ cout<<'\n'; }
template <class T> void out(const T& t){ print(t); cout<<'\n'; }
template <class T> void vout(const T& t){ println(t); cout<<'\n'; }
template <class Head, class... Tail> void out(const Head& head, const Tail&... tail){ print(head); cout<<' '; out(tail...); }
template <class Head, class... Tail> void vout(const Head& head, const Tail&... tail){ println(head); cout<<'\n'; vout(tail...); }
void fix(short x){ cout << fixed << setprecision(x); }
void Alpha(){ cout << boolalpha; }
void Flush(){ flush(cout); }
}; // IO
using namespace IO;
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define UL(...) ul __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define LIN(str) string str; lin(str)
#define VEC(type,name,size) V<type> name(size); in(name)
#define WEC(type,name,h,w) V<V<type>> name(h,V<type>(w)); in(name)
#define fin(...) do{ out(__VA_ARGS__); return; }while(false)

namespace yesno_sys {
inline void YES(bool ok=1) { out(ok?"YES":"NO"); }
inline void NO(bool ok=1) { YES(!ok); }
inline void Yes(bool ok=1) { out(ok?"Yes":"No"); }
inline void No(bool ok=1) { Yes(!ok); }
inline void yes(bool ok=1) { print(ok?"yes":"no"); }
inline void no(bool ok=1) { yes(!ok); }
}; // yesno_sys
using namespace yesno_sys;

#ifdef local
#include <debug_print.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) static_cast<void>(0)
#endif
#define elif else if
#define scp(a,x,b) a<=x&&x<=b
#define eid(el,v) &el-&v[0]
#define mp make_pair
#define mt make_tuple
#define gt(tpl,x) get<x>(tpl)
#define bif(bit,tar) (tar>>bit)&1
#define nxp(x) next_permutation(all(x))
#define prp(x) prev_permutation(all(x))
#define strpl(s,a,b) regex_replace(s,regex(a),b)
#define rgxmt(s,rgx) regex_match(s,regex(rgx))
namespace zia_qu {
template <class T> inline T sqr(T x){ return x*x; }
template <class T> inline T cub(T x){ return x*x*x; }
template <class T> inline T Mod(T x, T m){ return (x+m)%m; }
template <class T> inline T Pow(T a, T b, T mod=0) {
    T res=1;
    if(mod) {
        res%=mod;
        a%=mod;
    }
    while(b>0) {
        if(b&1) res*=a;
        if(mod) res%=mod;
        a*=a;
        if(mod) a%=mod;
        b>>=1;
    }
    return res;
}
inline ll Ceil(ld x, ll m){ return ceil(x/m); }
inline ll Round(ld x, ll m, short fx=0){ if(fx==0) return round(x/m); else { ul y=Pow<ul>(10,fx); return round((x/y)/m)*y; } }
inline ld Log(ll x, double base=2){ return log2(x)/log2(base); }
inline int bitdigit(ll x){ return 64-__builtin_clzll(x); }
inline int popcnt(ll x){ return __builtin_popcountll(x); }
inline bool popcnt_OE(ll x){ return __builtin_parityll(x); }
inline int fione(ll x){ return __builtin_ffsll(x); }
inline int zrcnt(ll x){ return __builtin_ctzll(x); }
inline bool isupper(char c){ return std::isupper(c); }
inline bool isupper(string s){ bool ok=1; each(el,s) ok&=isupper(el); return ok; }
inline bool islower(char c){ return std::islower(c); }
inline bool islower(string s){ bool ok=1; each(el,s) ok&=islower(el); return ok; }
inline bool isalpha(char c){ return std::isalpha(c); }
inline bool isalpha(string s){ bool ok=1; each(el,s) ok&=isalpha(el); return ok; }
inline bool isalnum(char c){ return std::isalnum(c); }
inline bool isalnum(string s){ bool ok=1; each(el,s) ok&=isalnum(el); return ok; }
inline bool isspace(char c){ return std::isspace(c); }
inline bool isspace(string s){ bool ok=1; each(el,s) ok&=isspace(el); return ok; }
inline bool ispunct(char c){ return std::ispunct(c); }
inline bool ispunct(string s){ bool ok=1; each(el,s) ok&=ispunct(el); return ok; }
inline bool isprint(char c){ return std::isprint(c); }
inline bool isprint(string s){ bool ok=1; each(el,s) ok&=isprint(el); return ok; }
inline void strins(string &s, string t, ll id){ s.insert(id,t); }
inline string toupper(string s){ each(c,s) c=std::toupper(c); return s; }
inline string tolower(string s){ each(c,s) c=std::tolower(c); return s; }
inline vi ten_to_adic(ll m, ll n) {
    vi res;
    ll now=m;
    while(now!=0) {
        res.emplace_back(now%n);
        now/=n;
    }
    //rev(res);
    return res;
}
inline ll adic_to_ten(vi &v, ll u) {
    ll res=0;
    //rev(v);
    each(el,v) {
        ll idx=eid(el,v);
        res+=Pow(u,idx)*el;
    }
    return res;
}
inline string to_hex(ll x) {
    stringstream ss;
    ss<<hex<<x;
    string s=ss.str();
    //s=toupper(s);
    return s;
}
inline string to_oct(ll x) {
    stringstream s;
    s<<oct<<x;
    return s.str();
}
inline string to_bin(ll x) {
    stringstream ss;
    ss<<bitset<64>(x);
    string s=ss.str();
    reverse(all(s));
    s.resize(ten_to_adic(x,2).size());
    reverse(all(s));
    return s;
}
inline ll to_ten(string s, short base){ return stoll(s,nullptr,base); }
template <class... Ts> constexpr auto symin(Ts... a){ return min(initializer_list<common_type_t<Ts...>>{a...}); }
template <class... Ts> constexpr auto symax(Ts... a){ return max(initializer_list<common_type_t<Ts...>>{a...}); }
template<class K, class U> inline V<K> kyl(const map<K,U> m, const U val) {
    V<K> keys;
    irp(it,m) {
        if(it->second==val) keys.emplace_back(it->first);
    }
    return keys;
}
#define stmin(st) *st.begin()
#define stmax(st) *st.rbegin()
#define kymin(m) m.begin()->first
#define kymax(m) m.rbegin()->first
#define kymin_v(m) m.begin()->second
#define kymax_v(m) m.rbegin()->second
template <class K, class V> inline V vlmin(map<K,V> &m){
    auto pr = *min_element(all(m),[](P<K,V> const &x, P<K,V> const &y){ return x.second > y.second; });
    return pr.second;
}
template <class K, class V> inline V vlmax(map<K,V> &m){
    auto pr = *max_element(all(m),[](P<K,V> const &x, P<K,V> const &y){ return x.second < y.second; });
    return pr.second;
}
template <class K, class V> inline K vlmin_k(map<K,V> &m){
    auto pr = *min_element(all(m),[](P<K,V> const &x, P<K,V> const &y){ return x.second > y.second; });
    return pr.first;
}
template <class K, class V> inline K vlmax_k(map<K,V> &m){
    auto pr = *max_element(all(m),[](P<K,V> const &x, P<K,V> const &y){ return x.second < y.second; });
    return pr.first;
}
}; // zia qu

namespace Lady_sANDy {
template <class T> inline void rev(T& v){ reverse(all(v)); }
template <class T> inline void rev(T& v, ll a, ll b){ reverse(all(v,a,b)); }
template <class T> inline void Sort(T& v){ sort(all(v)); }
template <class T> inline void Sort(T& v, ll a, ll b){ sort(all(v,a,b)); }
template <class T> inline void Sortt(T& v){ sort(rall(v)); }
template <class T> inline void Sortt(T& v, ll a, ll b){ sort(rall(v,a,b)); }
template <class T> inline void Sorth(T& v){ make_heap(all(v)); sort_heap(all(v)); }
template <class T, class I> inline ll dst(T& v, I itr){ return distance(v.begin(),itr); }
template <class T> inline T mrg(T& a, T& b){ T res; merge(all(a),all(b),back_inserter(res)); return res; }
template <class T> inline T Min(const V<T>& v){ return *min_element(all(v)); }
template <class T> inline T Max(const V<T>& v){ return *max_element(all(v)); }
template <class T> inline ll Min_i(const T& v){ return dst(v,min_element(all(v))); }
template <class T> inline ll Max_i(const T& v){ return dst(v,max_element(all(v))); }
template <class T, class U> inline ll LB(const T& v, const U x){ return dst(v,lower_bound(all(v),x)); }
template <class T, class U> inline ll UB(const T& v, const U x){ return dst(v,upper_bound(all(v),x)); }
template <class T, class U> inline bool BS(const T& v, const U x){ return binary_search(all(v),x); }
template <class T, class U, class Boolean> inline bool BS(const T& v, const U x, Boolean fn){ return binary_search(all(v),x,fn); }
template <class T, class Boolean> inline bool All(const T& v, Boolean fn){ return all_of(all(v),fn); }
template <class T, class Boolean> inline bool Exist(const T& v, Boolean fn){ return any_of(all(v),fn); }
template <class T, class Boolean> inline void pt(T& v, Boolean fn){ partition(all(v),fn); }
template <class T, class Boolean> inline ll ptp(T& v, Boolean fn){ return dst(v,partition_point(all(v),fn)); }
template <class T, class U> inline ll Find(T& v, const U x){ auto itr=find(all(v),x); if(itr==v.end()) return -1LL; return dst(v,itr); }
template <class T, class U> inline void rpl(T& v, U fn, U r){ replace(all(v),fn,r); }
template <class T, class Boolean, class U> inline void rplif(T& v, Boolean fn, U r){ replace_if(all(v),fn,r); }
template <class T, class Boolean> inline ul cntif(T& v, Boolean fn){ return count_if(all(v),fn); }
template <class T> inline T Count(V<T>& v, ll x) { /*Sort(v);//*/ return UB(v,x)-LB(v,x); }
template <class T> inline T IP(const V<T>& v, const V<T>& u, T init){ return inner_product(all(v),u.begin(),init); }
template <class T> inline V<T> iot(T n, ll init=0){ V<T> a(n); iota(all(a),init); return a;}
template <class T> inline ll vins(V<T>& v, T x, ll id){ v.insert(v.begin()+id,x); return v.size(); }
template <class T, class U> inline ll vins(T& v, U u, ll id){ v.insert(v.begin()+id,all(u)); return v.size(); }
template <class T, class U> inline ll vins(T& v, U u, ll id, ll a, ll b){ v.insert(v.begin()+id,all(u,a,b)); return v.size(); }
template <class T, class U> inline ll ers(T& v, U x){ v.erase(remove(all(v),x),v.end()); return v.size(); }
template <class T, class Boolean> ll ersif(T& v, Boolean x){ v.erase(remove_if(all(v),x),v.end()); return v.size(); }
template <class T> inline ll unq(T& v){ Sort(v); v.erase(unique(all(v)),v.end()); return v.size(); }
template <class T> inline T cp(const T& v){ T res; copy(all(v),back_inserter(res)); return res; }
template <class T> inline T cp(const T& v, ll a, ll b){ T res; copy(all(v,a,b),back_inserter(res)); return res; }
template <class T> inline void rtt(T& s, ll idx){ ll id=zia_qu::Mod<ll>(idx,s.size()); rotate(all(s,id),s.end());  }
template <class T> inline void rtt(T& s, ll a, ll b, ll c){ rotate(all(s,a,b),s.end()-c);  }
template <class T> inline V<T> psum(V<T>& v) {
    V<T> s(v.size()+1);
    partial_sum(all(v),s.begin());
    rtt(s,-1);
    return s;
}
template <class T> inline V<T> adf(V<T>& v) {
    V<T> res(v.size());
    adjacent_difference(all(v),res.begin());
    rtt(res, 1);
    res.resize(v.size()-1);
    return res;
}
#ifdef local
#define rext(...) static_cast<vi>(0)
template <class T> inline ll vsum(V<T> &v){ return accumulate(all(v),0LL); }
template <class T> inline ll vsum(V<T> &v, ll a, ll b){ return accumulate(all(v,a,b),0LL); }
template <class T> inline ld vdsum(V<T> &v){ return accumulate(all(v),0.0L); }
template <class T> inline ld vdsum(V<T> &v, ll a, ll b){ return accumulate(all(v,a,b),0.0L); }
template <class T> inline ll vmul(V<T> &v){ return accumulate(all(v),1LL,[](ll acc,ll i){ return acc*i; }); }
template <class T> inline ll vmul(V<T> &v, ll a, ll b){ return accumulate(all(v,a,b),1LL,[](ll acc,ll i){ return acc*i; }); }
template <class T> inline ld vdmul(V<T> &v){ return accumulate(all(v),1.0L,[](ll acc,ll i){ return acc*i; }); }
template <class T> inline ld vdmul(V<T> &v, ll a, ll b){ return accumulate(all(v,a,b),1.0L,[](ll acc,ll i){ return acc*i; }); }
#else
template <class T> inline V<T> rext(V<T>& v, mt19937 eng, ll size){ V<T> res; sample(all(v),back_inserter(res),size,eng); return res; }
template <class T> inline T rext(V<T>& v, mt19937 eng){ V<T> res; sample(all(v),back_inserter(res),1,eng); return res.front(); }
template <class T> inline ll vsum(V<T> &v){ return reduce(all(v),0LL); }
template <class T> inline ll vsum(V<T> &v, ll a, ll b){ return reduce(all(v,a,b),0LL); }
template <class T> inline ld vdsum(V<T> &v){ return reduce(all(v),0.0L); }
template <class T> inline ld vdsum(V<T> &v, ll a, ll b){ return reduce(all(v,a,b),0.0L); }
template <class T> inline ll vmul(V<T> &v){ return reduce(all(v),1LL,[](ll acc,ll i){ return acc*i; }); }
template <class T> inline ll vmul(V<T> &v, ll a, ll b){ return reduce(all(v,a,b),1LL,[](ll acc,ll i){ return acc*i; }); }
template <class T> inline ld vdmul(V<T> &v){ return reduce(all(v),1.0L,[](ll acc,ll i){ return acc*i; }); }
template <class T> inline ld vdmul(V<T> &v, ll a, ll b){ return reduce(all(v,a,b),1.0L,[](ll acc,ll i){ return acc*i; }); }
#endif
}; // Lady s&y

namespace Heileden {
/* BFS Sample
template <class T> inline void bfs(V<V<T>>& g, T start, vb& visited) {
    queue<T> que;
    que.emplace(start);
    visited[start]=1;
    while(!que.empty()) {
        T v=que.front();
        que.pop();
        each(nv,g[v]) {
            if(!visited[nv]) {
                visited[nv]=1;
                que.emplace(nv);
            }
        }
    }
}//*/

/* DFS Sample
template <class T> inline void dfs(V<V<T>>& g, T v, vb& visited) {
    visited[v]=1;
    each(nv,g[v]) if(!visited[nv]) dfs(g,nv,visited);
}//*/

/* Permutation Sample
template <class T> inline void nPr(V<T>& v) {
    Sort(v);
    do {out(v);} while(nxp(v));
}//*/

/* Binary Search Sample
template <class T, class U> inline ll MGRBS(T v, U x, ll& ng, ll& ok) {
    while(abs(ok-ng)>1) {
        ll mid = (ok+ng)/2;
        if(v[mid]==x) ok=mid;
        else ng=mid;
    }
    return ok;
}//*/

/* Dijikstra-like Sample
template <class T> inline T dijikstra(const V<T>& v) {
    pqr<T> pq;
    T res=0;
    while(!pq.empty()) {
        each(el,v) pq.emplace(el+res);
        res=pq.top();
        pq.pop();
    }
    return res;
}//*/

// divisor
template <class T> inline V<T> divisor(T n) {
    V<T> div;
    sqrp(i,1,n) {
        if(n%i==0) {
            div.emplace_back(i);
            if(i*i!=n) div.emplace_back(n/i);
        }
    }
    Lady_sANDy::Sort(div);
    return div;
}

// prime judge
inline bool is_prime(ul n) {
    if(n==1) return 0;
    sqrp(i,2,n) if(n%i==0) return 0;
    return 1;
}

// Siege of Eratosthenes
inline vb SoE(ll n) {
    vb prime(n+1,1);
    if(n>=0) prime[0]=0;
    if(n>=1) prime[1]=0;
    sqrp(i,2,n) {
        if(!prime[i]) continue;
        rep(j,i*i,n+1,i) prime[j]=0;
    }
    return prime;
}

// prime factor
template <class T> inline V<PP<T>> prmfct(T n) {
    V<PP<T>> res;
    rep(i,2,n+1) {
        if(n%i!=0) continue;
        T tmp=0;
        while(n%i==0) {
            tmp++;
            n/=i;
        }
        res.emplace_back(i,tmp);
    }
    if(n!=1) res.emplace_back(n,1);
    return res;
}

// Manacher
V<int> manacher(const string &s) {
    const int n = s.size();
    V<int> radius(n);
    int i = 0, j = 0;
    while(i < n) {
        while(i - j >= 0 && i + j < n && s[i - j] == s[i + j]) ++j;
        radius[i] = j;
        int k = 1;
        while(i - k >= 0 && i + k < n && k + radius[i - k] < j) {
            radius[i + k] = radius[i - k];
            ++k;
        }
        i += k;
        j -= k;
    }
    return radius;
}

// factorial
template <class T> T factor(T n) {
    T res=1;
    while(n>0) res*=n--;
    return res;
}

// permutation
template <class T=ll> T perm(T n, T r) {
    T tmp=n;
    T res=1;
    while(n>tmp-r) res*=n--;
    return res;
}

// binomial
template <class T=ll> T binom(T n, T r) {
    if(r < 0 || n < r) return 0;
    T ret = 1;
    rep(i,1,r) {
        ret *= n--;
        ret /= i;
    }
    return ret;
}

// integer judge
inline bool is_int(ld n){ ll r=floor(n); return r==n; }
inline bool is_sqr(ll n){ return is_int(sqrt(n)); }

/* grundy sample
template <class T> inline bool grundy(V<T> v) {
    ll res=0;
    each(el,v) res^=el;
    return res!=0;
}//*/
}; // Heileden

//constexpr const int mod=MOD;
constexpr const int mod=M0D;
struct mint{
    uint num = 0;
    constexpr mint() noexcept {}
    constexpr mint(const mint &x) noexcept : num(x.num){}
    constexpr operator ll() const noexcept { return num; }
    constexpr mint& operator+=(mint x) noexcept { num += x.num; if(num >= mod) num -= mod; return *this; }
    constexpr mint& operator++() noexcept { if(num == mod - 1) num = 0; else num++; return *this; }
    constexpr mint operator++(int) noexcept { mint ans(*this); operator++(); return ans; }
    constexpr mint operator-() const noexcept { return mint(0) -= *this; }
    constexpr mint& operator-=(mint x) noexcept { if(num < x.num) num += mod; num -= x.num; return *this; }
    constexpr mint& operator--() noexcept { if(num == 0) num = mod - 1; else num--; return *this; }
    constexpr mint operator--(int) noexcept { mint ans(*this); operator--(); return ans; }
    constexpr mint& operator*=(mint x) noexcept { num = ul(num) * x.num % mod; return *this; }
    constexpr mint& operator/=(mint x) noexcept { return operator*=(x.inv()); }
    template<class T> constexpr mint(T x) noexcept {
        using U = typename conditional<sizeof(T)>= 4, T, int>::type;
        U y = x; y %= U(mod); if(y < 0) y += mod; num = uint(y);
    }
    template <class T> constexpr mint operator+(T x) const noexcept { return mint(*this) += x; }
    template <class T> constexpr mint& operator+=(T x) noexcept { return operator+=(mint(x)); }
    template <class T> constexpr mint operator-(T x) const noexcept { return mint(*this) -= x; }
    template <class T> constexpr mint& operator-=(T x) noexcept { return operator-=(mint(x)); }
    template <class T> constexpr mint operator*(T x) const noexcept { return mint(*this) *= x; }
    template <class T> constexpr mint& operator*=(T x) noexcept { return operator*=(mint(x)); }
    template <class T> constexpr mint operator/(T x) const noexcept { return mint(*this) /= x; }
    template <class T> constexpr mint& operator/=(T x) noexcept { return operator/=(mint(x)); }
    constexpr mint inv() const noexcept { ll x = 0, y = 0; extgcd(num, mod, x, y); return x; }
    static constexpr ll extgcd(ll a, ll b, ll &x, ll &y) noexcept { ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; }
    constexpr mint pow(ul x) const noexcept { mint ans = 1, cnt = *this; while(x){ if(x & 1) ans *= cnt; cnt *= cnt; x /= 2; } return ans; }
    friend ostream& operator<<(ostream& os, const mint& m){ os << m.num; return os; }
    friend istream &operator>>(istream &is, mint &a) {
        ll t;
        is >> t;
        a=mint(t);
        return (is);
    }
};
#define MINT(...) mint __VA_ARGS__; in(__VA_ARGS__)
using vm = V<mint>;
using wm = V<vm>;
using pm = PP<mint>;
vm fac(1,1),inv(1,1);
void reserve(ll a){
    if(fac.size()>=a) return;
    if(a<fac.size()*2) a=fac.size()*2;
    if(a>=mod) a=mod;
    while(fac.size()<a) fac.emplace_back(fac.back()*mint(fac.size()));
    inv.resize(fac.size());
    inv.back()=fac.back().inv();
    for(ll i=inv.size()-1; !inv[i-1]; i--) inv[i-1]=inv[i]*i;
}
mint fact(ll n){ if(n<0) return 0; reserve(n + 1); return fac[n]; }
mint nPr(ll n,ll r){
    if(r<0 || n<r) return 0;
    if(n>>24){ mint ans=1; rep(r) ans*=n--; return ans; }
    reserve(n+1); return fac[n]*inv[n-r];
}
mint nCr(ll n,ll r){ if(r<0 || n<r) return 0; r=min(r,n-r); reserve(r+1); return nPr(n,r)*inv[r]; }
mint nHr(ll n,ll r){ if(!n && !r) return 1; if(n<=0 || r<0) return 0; return nCr(n+r-1,r); }

// --------------------------------------------------------------------------------------------------------------

using namespace zia_qu;
using namespace Lady_sANDy;
using namespace Heileden;

int main() {
    VvyLw::Twitter::wa_haya_exe();
    /*INT(t); while(t--)//*/
    VvyLw::solve();
}

// --------------------------------------------------------------------------------------------------------------


void VvyLw::solve() {
    LL(n,k);
    auto f=[](mint x) {
        auto pr=prmfct(x);
        each(el,pr) {
            el.first++;
        }
        mint res=1;
        each(fi,se,pr) {
            res*=fi.pow(se);
        }
        return res;
    };
    mint ans=n;
    rep(k) {
        ans=f(ans);
    }
    out(ans);
}