#include<cassert>
#include <bits/stdc++.h>
#ifndef IO_HPP
#define IO_HPP
#include<iostream>
#include<vector>
#include<queue>
#include<stack>
#include<array>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
using namespace std;
template<typename T1,typename T2>istream &operator>>(istream&,pair<T1,T2>&);
template<typename...Args>istream &operator>>(istream&,tuple<Args...>&a);
template<typename T>istream &operator>>(istream&is,vector<T>&a);
template<typename T,size_t N>istream &operator>>(istream&is,array<T,N>&a);
template<typename T1,typename T2>
istream &operator>>(istream&is,pair<T1,T2>&a){
  is>>a.first>>a.second;
  return is;
}
template<size_t pos,typename...Args>
void read_tuple(istream&is,tuple<Args...>&a){
  if constexpr(pos<tuple_size<tuple<Args...>>::value){
    is>>get<pos>(a);
    read_tuple<pos+1>(is,a);
  }
}
template<typename...Args>
istream &operator>>(istream&is,tuple<Args...>&a){
  read_tuple<0>(is,a);
  return is;
}
template<typename T>
istream &operator>>(istream&is,vector<T>&a){
  for(T&x:a)is>>x;
  return is;
}
template<typename T,size_t N>
istream &operator>>(istream&is,array<T,N>&a){
  for(T&x:a)is>>x;
  return is;
}
template<typename T1,typename T2>ostream &operator<<(ostream&os,const pair<T1,T2>&);
template<typename...Args>ostream &operator<<(ostream&os,const tuple<Args...>&);
template<typename T>ostream &operator<<(ostream&os,const vector<T>&);
template<typename T,typename Seq,typename Comp>ostream &operator<<(ostream&os,priority_queue<T,Seq,Comp>);
template<typename T>ostream &operator<<(ostream&os,queue<T>);
template<typename T>ostream &operator<<(ostream&os,deque<T>);
template<typename T>ostream &operator<<(ostream&os,stack<T>);
template<typename T,size_t N>ostream &operator<<(ostream&os,const array<T,N>&);
template<typename Key,typename Val,typename Comp>ostream &operator<<(ostream&os,const map<Key,Val,Comp>&);
template<typename Key,typename Val,typename Hash>ostream &operator<<(ostream&os,const unordered_map<Key,Val,Hash>&);
template<typename T,typename Comp>ostream &operator<<(ostream&os,const set<T,Comp>&);
template<typename T,typename Comp>ostream &operator<<(ostream&os,const multiset<T,Comp>&);
template<typename T,typename Hash>ostream &operator<<(ostream&os,const unordered_set<T,Hash>&);
template<typename T1,typename T2>
ostream &operator<<(ostream&os,const pair<T1,T2>&a){
  os<<a.first<<' '<<a.second;
  return os;
}
template<size_t pos,typename...Args>
void write_tuple(ostream&os,const tuple<Args...>&a){
  if constexpr(pos<tuple_size<tuple<Args...>>::value){
    if constexpr(pos>0)os<<' ';
    os<<get<pos>(a);
    write_tuple<pos+1>(os,a);
  }
}
template<typename...Args>
ostream &operator<<(ostream&os,const tuple<Args...>&a){
  write_tuple<0>(os,a);
  return os;
}
template<typename T>
ostream &operator<<(ostream&os,const vector<T>&a){
  os<<'{';
  for(int i=0;i<(int)a.size();i++){
    os<<a[i];
    if(i+1!=a.size())os<<',';
  }
  os<<'}';
  return os;
}
template<typename T,typename Seq,typename Comp>
ostream &operator<<(ostream&os,priority_queue<T,Seq,Comp>a){
  os<<'{';
  if(!a.empty()){
    os<<a.top();a.pop();
    while(!a.empty()){
      os<<',';
      os<<a.top();
      a.pop();
    }
  }
  os<<'}';
  return os;
}
template<typename T>
ostream &operator<<(ostream&os,queue<T>a){
  os<<'{';
  if(!a.empty()){
    os<<a.front();a.pop();
    while(!a.empty()){
      os<<',';
      os<<a.front();
      a.pop();
    }
  }
  os<<'}';
  return os;
}
template<typename T>
ostream &operator<<(ostream&os,deque<T>a){
  os<<'{';
  if(!a.empty()){
    os<<a.front();a.pop_front();
    while(!a.empty()){
      os<<',';
      os<<a.front();
      a.pop_front();
    }
  }
  os<<'}';
  return os;
}
template<typename T>
ostream &operator<<(ostream&os,stack<T>a){
  os<<'{';
  if(!a.empty()){
    os<<a.top();a.pop();
    while(!a.empty()){
      os<<',';
      os<<a.top();
      a.pop();
    }
  }
  os<<'}';
  return os;
}
template<typename T,size_t N>
ostream &operator<<(ostream&os,const array<T,N>&a){
  os<<'{';
  for(int i=0;i<(int)a.size();i++){
    os<<a[i];
    if(i+1!=a.size())os<<',';
  }
  os<<'}';
  return os;
}
template<typename Key,typename Val,typename Comp>
ostream &operator<<(ostream&os,const map<Key,Val,Comp>&a){
  if(a.empty()){
    os<<"{}";
    return os;
  }
  auto itr=a.begin();
  os<<"{["<<itr->first<<","<<itr->second<<']';
  while(++itr!=a.end())os<<",["<<itr->first<<','<<itr->second<<']';
  os<<'}';
  return os;
}
template<typename Key,typename Val,typename Hash>
ostream &operator<<(ostream&os,const unordered_map<Key,Val,Hash>&a){
  if(a.empty()){
    os<<"{}";
    return os;
  }
  auto itr=a.begin();
  os<<"{["<<itr->first<<","<<itr->second<<']';
  while(++itr!=a.end())os<<",["<<itr->first<<','<<itr->second<<']';
  os<<'}';
  return os;
}
template<typename T,typename Comp>
ostream &operator<<(ostream&os,const set<T,Comp>&a){
  if(a.empty()){
    os<<"{}";
    return os;
  }
  auto itr=a.begin();
  os<<'{'<<*itr;
  while(++itr!=a.end())os<<','<<*itr;
  os<<'}';
  return os;
}
template<typename T,typename Comp>
ostream &operator<<(ostream&os,const multiset<T,Comp>&a){
  if(a.empty()){
    os<<"{}";
    return os;
  }
  auto itr=a.begin();
  os<<'{'<<*itr;
  while(++itr!=a.end())os<<','<<*itr;
  os<<'}';
  return os;
}
template<typename T,typename Hash>
ostream &operator<<(ostream&os,const unordered_set<T,Hash>&a){
  if(a.empty()){
    os<<"{}";
    return os;
  }
  auto itr=a.begin();
  os<<'{'<<*itr;
  while(++itr!=a.end())os<<','<<*itr;
  os<<'}';
  return os;
}
#endif
using namespace std;
using ll=long long;
using ull=unsigned long long;
using P=pair<ll,ll>;
template<typename T>using minque=priority_queue<T,vector<T>,greater<T>>;
template<typename T>bool chmax(T &a,const T &b){return (a<b?(a=b,true):false);}
template<typename T>bool chmin(T &a,const T &b){return (a>b?(a=b,true):false);}
template<typename T1,typename T2>void operator++(pair<T1,T2>&a,int){a.first++,a.second++;}
template<typename T1,typename T2>void operator--(pair<T1,T2>&a,int){a.first--,a.second--;}
template<typename T>void operator++(vector<T>&a,int){for(auto &i:a)i++;}
template<typename T>void operator--(vector<T>&a,int){for(auto &i:a)i--;}
using vref=typename vector<bool>::reference;
vref operator|=(vref a,bool b){a=a|b;return a;}
vref operator&=(vref a,bool b){a=a&b;return a;}
vref operator^=(vref a,bool b){a=a^b;return a;}
#define overload3(_1,_2,_3,name,...) name
#define rep1(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++)
#define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__)
#define reps(i,l,r) rep2(i,l,r)
#define all(x) x.begin(),x.end()
#define pcnt(x) __builtin_popcountll(x)
#define fin(x) return cout<<(x)<<'\n',static_cast<void>(0)
#define yn(x) cout<<((x)?"Yes\n":"No\n")
#define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end())
template<typename T>
inline int fkey(vector<T>&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();}
ll myceil(ll a,ll b){return (a+b-1)/b;}
template<typename T,size_t n,size_t id=0>
auto vec(const int (&d)[n],const T &init=T()){
  if constexpr (id<n)return vector(d[id],vec<T,n,id+1>(d,init));
  else return init;
}
#ifdef LOCAL
#include<debug.h>
#define SWITCH(a,b) (a)
#else
#define debug(...) static_cast<void>(0)
#define debugg(...) static_cast<void>(0)
#define SWITCH(a,b) (b)
#endif
struct Timer{
  clock_t start;
  Timer(){
    start=clock();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout<<fixed<<setprecision(16);
  }
  inline double now(){return (double)(clock()-start)/1000;}
  #ifdef LOCAL
  ~Timer(){
    cerr<<"time:";
    cerr<<now();
    cerr<<"ms\n";
  }
  #endif
}timer;
void SOLVE();
int main(){
  int testcase=1;
  //cin>>testcase;
  for(int i=0;i<testcase;i++){
    SOLVE();
  }
}
#include<type_traits>
#include<optional>
#include<initializer_list>
constexpr bool isprime_constexpr(unsigned long long n){
  if(n==998244353)return true;
  if(n==1000000007)return true;
  if(n<64)return 2891462833508853932ll>>n&1;
  if(n%2==0)return false;
  unsigned long long d=n-1;
  int s=0;
  while(!(d&1))d>>=1,s++;
  int q=63;
  while(!(d>>q))q--;
  unsigned long long r=n;
  for(int i=0;i<5;i++)r*=2-r*n;
  auto redc=[&r,&n](__uint128_t x)->unsigned long long {
    x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64;
    return x>=n?x-n:x;
  };
  __uint128_t r2=-__uint128_t(n)%n;
  unsigned long long one=redc(r2);
  for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){
    if(base%n==0)continue;
    unsigned long long a=base=redc((base%n)*r2);
    for(int i=q-1;i>=0;i--){
      a=redc(__uint128_t(a)*a);
      if(d>>i&1)a=redc(__uint128_t(a)*base);
    }
    if(a==one)continue;
    for(int i=1;a!=n-one;i++){
      if(i>=s)return false;
      a=redc(__uint128_t(a)*a);
    }
  }
  return true;
}
constexpr std::pair<long long,long long>ext_gcd(long long a,long long b){
  if(b==0)return std::make_pair(1,0);
  auto [x,y]=ext_gcd(b,a%b);
  std::swap(x,y);
  return std::make_pair(x,y-a/b*x);
}
template<std::signed_integral T>
constexpr std::pair<T,T> inv_mod(T a,T b){
  a%=b;
  if(a<0)a+=b;
  if(a==0)return std::make_pair(b,0);
  T s=b,t=a;
  T m0=0,m1=1;
  while(t){
    T u=s/t;
    s-=t*u;
    m0-=m1*u;
    std::swap(s,t);
    std::swap(m0,m1);
  }
  if(m0<0)m0+=b/s;
  return std::make_pair(s,m0);
}
template<auto m>
struct modint{
  static_assert(1<=m&&m<(1ull<<63));
  using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>;
  using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>;
private:
  value_type v;
  static constexpr value_type umod=m;
  constexpr modint sqrt_impl()const{
    if(this->val()<=1)return *this;
    if(umod%8==1){
      modint b=2;
      while(b.pow((umod-1)/2).val()==1)b++;
      value_type m2=umod-1;
      int e=0;
      while(m2%2==0)m2>>=1,e++;
      modint x=this->pow((m2-1)/2);
      modint y=(*this)*x*x;
      x*=*this;
      modint z=b.pow(m2);
      while(y.val()!=1){
        int j=0;
        modint t=y;
        while(t.val()!=1)t*=t,j++;
        z=z.pow((value_type(1))<<(e-j-1));
        x*=z;
        z*=z;
        y*=z;
        e=j;
      }
      return x;
    }
    else if(umod%8==5){
      modint res=this->pow((umod+3)/8);
      if((res*res).val()==this->val())return res;
      else return res*modint(2).pow((umod-1)/4);
    }
    else return this->pow((umod+1)/4);
  }
  template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
  static constexpr value_type take_mod(U x){
    if constexpr(std::numeric_limits<U>::max()<umod)return x;
    if constexpr(umod==(1ull<<61)-1){
      value_type res=(x>>61)+(x&umod);
      if(res>=umod)res-=umod;
      return res;
    }
    if constexpr(umod==(1ull<<61)-(1ull<<24)+1){
      value_type high=x>>61,low=x&((1ull<<61)-1);
      mul_type t=low+(mul_type(high)<<24)-high;
      high=t>>61,low=t&((1ull<<61)-1);
      low=low+(mul_type(high)<<24)-high;
      if(low>=umod)low-=umod;
      return low;
    }
    return x%umod;
  }
public:
  constexpr modint():v(0){}
  template<typename U,std::enable_if_t<std::signed_integral<U>||std::is_same_v<U,__int128_t>,std::nullptr_t> =nullptr>
  constexpr modint(U x){
    x%=std::make_signed_t<value_type>(umod);
    v=x>=0?x:x+umod;
  }
  template<typename U,std::enable_if_t<std::unsigned_integral<U>||std::is_same_v<U,__uint128_t>,std::nullptr_t> =nullptr>
  constexpr modint(U x):v(take_mod<U>(x)){}
  static constexpr value_type mod(){return umod;}
  static constexpr modint zero(){return raw(0);}
  static constexpr modint one(){
    if constexpr(m==1)return raw(0);
    else return raw(1);
  }
  template<typename U>
  static constexpr modint raw(U x){
    modint res;
    res.v=x;
    return res;
  }
  constexpr std::make_signed_t<value_type> val()const{return v;}
  constexpr modint &operator+=(const modint&b){
    this->v+=b.v;
    if(this->v>=umod)this->v-=umod;
    return *this;
  }
  constexpr modint &operator-=(const modint&b){
    this->v-=b.v;
    if(this->v>=umod)this->v+=umod;
    return *this;
  }
  constexpr modint &operator*=(const modint&b){
    this->v=take_mod(mul_type(this->v)*mul_type(b.v));
    return *this;
  }
  constexpr modint &operator/=(const modint&b){return *this*=b.inv();}
  constexpr modint operator+()const{return *this;}
  constexpr modint operator-()const{return modint()-*this;}
  friend constexpr modint operator+(const modint&a,const modint&b){return modint(a)+=b;}
  friend constexpr modint operator-(const modint&a,const modint&b){return modint(a)-=b;}
  friend constexpr modint operator*(const modint&a,const modint&b){return modint(a)*=b;}
  friend constexpr modint operator/(const modint&a,const modint&b){return modint(a)/=b;}
  constexpr auto operator<=>(const modint&)const=default;
  constexpr modint operator++(int){
    modint res=*this;
    this->v++;
    if(this->v==umod)this->v=0;
    return res;
  }
  constexpr modint operator--(int){
    modint res=*this;
    if(this->v==0)this->v=umod;
    this->v--;
    return res;
  }
  template<std::integral U>
  constexpr modint pow(U k)const{
    if constexpr(std::is_signed_v<U>){
      assert(0<=k);
    }
    modint res=1,a(*this);
    while(k){
      if(k&1)res*=a;
      a*=a;
      k>>=1;
    }
    return res;
  }
  constexpr modint inv()const{
    if constexpr(isprime_constexpr(umod)){
      if(std::is_constant_evaluated()){
        if(v==0){
          throw "no inverse";
        }
      }
      else assert(v!=0);
      return pow(umod-2);
    }
    else{
      modint res;
      auto [g,x]=inv_mod<std::make_signed_t<value_type>>(this->v,umod);
      if(std::is_constant_evaluated()){
        if(g!=1){
          throw "no inverse";
        }
      }
      else assert(g==1);
      res.v=x;
      return res;
    }
  }
  std::optional<modint>sqrt()const{
    if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl());
    else return std::nullopt;
  }
  friend std::istream &operator>>(std::istream&is,modint&b){
    long long a;
    is>>a;
    b=modint(a);
    return is;
  }
  friend std::ostream &operator<<(std::ostream&os,const modint&b){
    os<<b.val();
    return os;
  }
};
template<auto m>
struct std::hash<modint<m>>{
  std::size_t operator()(modint<m>x)const{
    return std::hash<typename modint<m>::value_type>(x.val());
  }
};
using mint998=modint<998244353>;
using mint107=modint<1000000007>;
using mint61=modint<2305843009213693951>;
using mint6124=modint<2305843009196916737>;
struct is_modint_impl{
  template<typename T>
  static auto check(T&&x)->decltype(x.mod(),std::true_type{});
  template<typename T>
  static auto check(...)->std::false_type;
};
template<typename T>
struct is_modint:public decltype(is_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_modint_v=is_modint<T>::value;
struct is_dynamic_modint_impl{
  template<typename T>
  static auto check(T&&x)->decltype(x.set_mod((typename T::value_type)0),std::true_type{});
  template<typename T>
  static auto check(...)->std::false_type;
};
template<typename T>
struct is_dynamic_modint:public decltype(is_dynamic_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_dynamic_modint_v=is_dynamic_modint<T>::value;
template<typename T>
inline constexpr bool is_static_modint_v=is_modint_v<T>&&!is_dynamic_modint_v<T>;
struct is_uso_modint_impl{
  template<typename T>
  static auto check(T&&x)->decltype(x.uso(),std::true_type{});
  template<typename T>
  static auto check(...)->std::false_type;
};
template<typename T>
struct is_uso_modint:public decltype(is_uso_modint_impl::check<T>(std::declval<T>())){};
template<typename T>
inline constexpr bool is_uso_modint_v=is_uso_modint<T>::value;
template<typename T>
struct F{
private:
  static int capacity;
  static std::vector<T>fact,factinv,inv;
public:
  static void resize(int n){
    if(capacity>=n)return;
    fact.resize(n+1),factinv.resize(n+1),inv.resize(n+1);
    for(int i=capacity+1;i<=n;i++){
      fact[i]=fact[i-1]*T::raw(i);
      if constexpr(is_uso_modint_v<T>)inv[i]=T(1)/T(i);
      else inv[i]=-inv[T::mod()%i]*(T::mod()/i);
      factinv[i]=factinv[i-1]*inv[i];
    }
    capacity=n;
  }
  static T C(int n,int k){
    if(n<k)return 0;
    if(k<0)return 0;
    resize(n);
    return fact[n]*factinv[k]*factinv[n-k];
  }
  static T P(int n,int k){
    if(n<k)return 0;
    if(k<0)return 0;
    resize(n);
    return fact[n]*factinv[n-k];
  }
  static T H(int n,int k){
    if(n==0&&k==0)return 1;
    return C(n+k-1,k);
  }
  static T factorial(int n){
    resize(n);
    return fact[n];
  }
  static T factorial_inv(int n){
    resize(n);
    return factinv[n];
  }
  static T inverse(int n){
    resize(n);
    return inv[n];
  }
  static T S(long long n,int k){
    if(n<0)return 0;
    if(n<k)return 0;
    T ret=0;
    resize(k);
    for(int i=0;i<=k;i++){
      ret+=fact[k]*factinv[i]*factinv[k-i]*T::raw(i).pow(n)*((k-i)&1?-1:1);
    }
    return ret*factinv[k];
  }
  template<typename... INT>
  static T O(INT...k){
    int n=0;
    for(int i:std::initializer_list<int>{k...}){
      if(i<0)return 0;
      n+=i;
    }
    resize(n);
    T ret=fact[n];
    for(int i:std::initializer_list<int>{k...})ret*=factinv[i];
    return ret;
  }
  static T rising_factorial(int x,int n){
    assert(n>=0);
    if(x>0){
      resize(x+n-1);
      return fact[x+n-1]*factinv[x-1];
    }
    else if(x+n>0)return T();
    else{
      resize(-x);
      T res=fact[-x]*factinv[-x-n];
      if(n&1)res=-res;
      return res;
    }
  }
  static T falling_factorial(int x,int n){return rising_factorial(x-n+1,n);}
};
template<typename T>int F<T>::capacity=1;
template<typename T>std::vector<T>F<T>::fact{1,1};
template<typename T>std::vector<T>F<T>::factinv{1,1};
template<typename T>std::vector<T>F<T>::inv{0,1};
#include<concepts>
template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>msb(T n){return n==0?-1:31-__builtin_clz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>msb(T n){return n==0?-1:63-__builtin_clzll(n);}

template<typename T>
constexpr std::enable_if_t<std::numeric_limits<T>::digits<=32,int>lsb(T n){return n==0?-1:__builtin_ctz(n);}
template<typename T>
constexpr std::enable_if_t<(std::numeric_limits<T>::digits>32),int>lsb(T n){return n==0?-1:__builtin_ctzll(n);}

template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>floor_pow2(T n){return n==0?0:T(1)<<msb(n);}

template<typename T>
constexpr std::enable_if_t<std::is_integral_v<T>,T>ceil_pow2(T n){return n<=1?1:T(1)<<(msb(n-1)+1);}

template<std::integral T>
constexpr T safe_div(T a,T b){return a/b-(a%b&&(a^b)<0);}
template<std::integral T>
constexpr T safe_ceil(T a,T b){return a/b+(a%b&&(a^b)>0);}
template<typename M>
struct BinaryIndexedTree{
private:
  using S=typename M::S;
  std::vector<S>dat;
  int z;
public:
  BinaryIndexedTree(){}
  explicit BinaryIndexedTree(int n):z(ceil_pow2(n)),dat(n,M::e()){}
  explicit BinaryIndexedTree(const std::vector<S>&init):z(ceil_pow2((int)init.size())),dat(init){
    for(int i=0;i<(int)dat.size();i++){
      int j=i+((i+1)&-(i+1));
      if(j<(int)dat.size())dat[j]=M::op(dat[i],dat[j]);
    }
  }
  BinaryIndexedTree(int n,S init):BinaryIndexedTree(std::vector<S>(n,init)){}
  inline void add(int i,S x){
    while(i<(int)dat.size()){
      dat[i]=M::op(dat[i],x);
      i+=(i+1)&-(i+1);
    }
  }
  inline S sum(int i)const{
    S res=M::e();
    while(i>0){
      res+=dat[i-1];
      i-=i&-i;
    }
    return res;
  }
  inline S sum(int l,int r)const{
    S lp=M::e(),rp=M::e();
    while(l<r){
      rp=M::op(dat[r-1],rp);
      r-=r&-r;
    }
    while(r<l){
      lp=M::op(dat[l-1],lp);
      l-=l&-l;
    }
    return M::op(M::inverse(lp),rp);
  }
  int lower_bound(S k)const{
    int res=0;
    for(int i=z;i>=1;i>>=1){
      if(res+i<=(int)dat.size()&&dat[res+i-1]<k){
        k-=dat[res+i-1];
        res+=i;
      }
    }
    return res;
  }
  friend std::ostream &operator<<(std::ostream &os,const BinaryIndexedTree&bit){
    os<<"{";
    for(int i=0;i<(int)bit.dat.size();i++)os<<bit.sum(i,i+1)<<",}"[i+1==(int)bit.dat.size()];
    if(bit.dat.empty())os<<"}";
    return os;
  }
};
template<typename T>
struct MonoidAdd{
  using S=T;
  static inline S op(S x,S y){return x+y;}
  static inline S e(){return T();}
  static inline S inverse(S x){return -x;}
  static inline void revS(S&x){}
  template<typename U>
  static inline S pow(S x,U p){return x*p;}
};
template<typename M>
struct LazySegmentTree{
private:
  using S=typename M::M1::S;
  using F=typename M::M2::S;
  int n,z;
  int log2n;
  std::vector<S>dat;
  std::vector<F>lazy;
  inline void propagate(int i,const F&f){
    dat[i]=M::act(dat[i],f);
    if(i<z)lazy[i]=M::M2::op(lazy[i],f);
  }
  inline void push(int i){
    if(i<z){
      propagate(i*2,lazy[i]);
      propagate(i*2+1,lazy[i]);
      lazy[i]=M::M2::e();
    }
  }
  inline void update(int i){
    dat[i]=M::M1::op(dat[i*2],dat[i*2+1]);
  }
  inline void path_push(int i){
    int l=lsb(i);
    for(int j=log2n;j>l;j--)push(i>>j);
  }
  inline void path_update(int i){
    int l=lsb(i);
    i>>=(l+1);
    while(i){
      update(i);
      i>>=1;
    }
  }
public:
  LazySegmentTree():n(0),z(0),log2n(0){}
  explicit LazySegmentTree(int n_):n(n_),z(ceil_pow2(n_)){
    log2n=msb(z);
    dat.resize(z*2,M::M1::e()),lazy.resize(z*2,M::M2::e());
  }
  explicit LazySegmentTree(const std::vector<S>&init):n(init.size()),z(ceil_pow2((int)init.size())){
    log2n=msb(z);
    dat.resize(z*2,M::M1::e()),lazy.resize(z*2,M::M2::e());
    for(int i=0;i<n;i++)dat[i+z]=init[i];
    for(int i=z-1;i>=1;i--)update(i);
  }
  LazySegmentTree(int n_,S init):LazySegmentTree(std::vector<S>(n_,init)){}
  void set(int i,const S&x){
    assert(0<=i&&i<n);
    i+=z;
    for(int j=log2n;j>0;j--)push(i>>j);
    dat[i]=x;
    i>>=1;
    while(i){
      update(i);
      i>>=1;
    }
  }
  S get(int i){
    assert(0<=i&&i<n);
    i+=z;
    for(int j=log2n;j>0;j--)push(i>>j);
    return dat[i];
  }
  void apply(int l,int r,const F&f){
    assert(0<=l&&l<=r&&r<=n);
    if(r==n)r=z;
    l+=z,r+=z;
    path_push(l),path_push(r);
    int l2=l,r2=r;
    while(l<r){
      if(l&1)propagate(l++,f);
      if(r&1)propagate(--r,f);
      l>>=1,r>>=1;
    }
    path_update(l2),path_update(r2);
  }
  S prod(int l,int r){
    assert(0<=l&&l<=r&&r<=n);
    if(r==n)r=z;
    l+=z,r+=z;
    path_push(l),path_push(r);
    S left=M::M1::e(),right=M::M1::e();
    while(l<r){
      if(l&1)left=M::M1::op(left,dat[l++]);
      if(r&1)right=M::M1::op(dat[--r],right);
      l>>=1,r>>=1;
    }
    return M::M1::op(left,right);
  }
  inline S all_prod()const{return dat[1];}
  template<typename Func>
  int max_right(int l,const Func&f){
    assert(0<=l&&l<=n);
    if(l==n)return n;
    l+=z;
    for(int i=log2n;i>=1;i--)push(l>>i);
    S now=M::M1::e();
    do{
      l>>=lsb(l);
      S nxt=M::M1::op(now,dat[l]);
      if(f(nxt))now=nxt,l++;
      else{
        while(l<z){
          push(l);
          l<<=1;
          nxt=M::M1::op(now,dat[l]);
          if(f(nxt))now=nxt,l++;
        }
        return l-z;
      }
    }while(l!=(l&-l));
    return n;
  }
  template<typename Func>
  int min_left(int r,const Func&f){
    assert(0<=r&&r<=n);
    if(r==0)return 0;
    r+=z;
    for(int i=log2n;i>=1;i--)push((r-1)>>i);
    S now=M::M1::e();
    do{
      r--;
      while(r>1&&(r&1))r>>=1;
      S nxt=M::M1::op(dat[r],now);
      if(f(nxt))now=nxt;
      else{
        while(r<z){
          push(r);
          r=(r<<1)+1;
          nxt=M::M1::op(dat[r],now);
          if(f(nxt))now=nxt,r--;
        }
        return r-z+1;
      }
    }while(r!=(r&-r));
    return 0;
  }
  std::vector<S>get_all(){
    for(int i=1;i<z;i++)push(i);
    return std::vector<S>(dat.begin()+z,dat.begin()+z+n);
  }
  friend std::ostream &operator<<(std::ostream&os,const LazySegmentTree&seg){
    std::vector<F>lazy2(seg.lazy);
    for(int i=0;i<seg.n;i++)lazy2[i+seg.z]=M::M2::e();
    for(int i=1;i<seg.z;i++){
      lazy2[i*2]=M::M2::op(lazy2[i*2],lazy2[i]);
      lazy2[i*2+1]=M::M2::op(lazy2[i*2+1],lazy2[i]);
    }
    os<<"{";
    for(int i=0;i<seg.n;i++)os<<M::act(seg.dat[i+seg.z],lazy2[i+seg.z])<<",}"[i+1==seg.n];
    if(seg.n==0)os<<"}";
    return os;
  }
  int size()const{return n;}
};
template<typename T>
struct MonoidMul{
  using S=T;
  static inline S op(S x,S y){return x*y;}
  static inline S e(){
    if constexpr(requires(){T::one();})return T::one();
    else return T(1);
  }
  static inline void revS(S&){}
  static inline S inverse(S x){return x.inv();}
};
using mint=mint998;
struct M{
  using M1=MonoidAdd<mint>;
  using M2=MonoidMul<mint>;
  static mint act(mint x,mint f){return x*f;}
};
mint calc(int n,int need,int m){
  if(n<need)return 0;
  mint res=0;
  rep(i,need+1){
    res+=F<mint>::C(need,i)*(i&1?-1:1)*mint(m-i).pow(n)/mint(m).pow(n);
  }
  return res;
}
void SOLVE(){
  int n,m;
  cin>>n>>m;
  vector<int>c(n);
  cin>>c;
  c--;
  int x=count(all(c),-1);
  mint ans=0;
  LazySegmentTree<M>seg_m(n);
  vector<vector<mint>>val(m,vector<mint>(n));
  vector<mint>val_sum(m);
  BinaryIndexedTree<MonoidAdd<int>>e_bit(n);
  vector<int>mask(n);
  vector<int>pos(m,n);
  int multi=0;
  vector<vector<mint>>mpow(m+1,vector<mint>(n+1)),mpowinv(m+1,vector<mint>(n+1));
  rep(i,m+1){
    mpow[i][0]=mpowinv[i][0]=1;
    mint v=mint(m-i)/m;
    rep(j,1,n+1){
      mpow[i][j]=mpow[i][j-1]*v;
    }
    if(i<m)rep(j,n+1)mpowinv[i][j]=mpow[i][j].inv();
  }
  auto eval=[&](int i)->void {
    int need=m-pcnt(mask[i]);
    int e=e_bit.sum(0,i+1);
    rep(j,need+1){
      if(j==m)seg_m.set(i,F<mint>::C(need,j)*(j&1?-1:1)*mpow[j][e]);
      else{
        val_sum[j]-=val[j][i];
        val[j][i]=F<mint>::C(need,j)*(j&1?-1:1)*mpow[j][e]*mpowinv[j][multi];
        val_sum[j]+=val[j][i];
      }
    }
    if(need+1<=m){
      if(need+1==m)seg_m.set(i,0);
      else{
        val_sum[need+1]-=val[need+1][i];
        val[need+1][i]=0;
      }
    }
  };
  for(int i=n-1;i>=0;i--){
    if(c[i]==-1){
      e_bit.add(i,1);
      multi++;
      eval(i);
      seg_m.apply(i+1,n,0);
    }
    else{
      rep(ii,i,pos[c[i]]){
        assert(!(mask[ii]>>c[i]&1));
        mask[ii]|=1<<c[i];
        eval(ii);
      }
      pos[c[i]]=i;
    }
    rep(j,m)ans+=val_sum[j]*mpow[j][multi];
    ans+=seg_m.all_prod();
  }
  ans*=mint(m).pow(x);
  cout<<ans<<endl;
}