結果
| 問題 | No.1321 塗るめた |
| ユーザー |
 hotman78
|
| 提出日時 | 2020-12-18 00:47:51 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 72 ms / 2,000 ms |
| コード長 | 44,877 bytes |
| コンパイル時間 | 6,790 ms |
| コンパイル使用メモリ | 309,852 KB |
| 実行使用メモリ | 24,620 KB |
| 最終ジャッジ日時 | 2024-09-21 08:45:24 |
| 合計ジャッジ時間 | 9,216 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 17 ms
18,944 KB |
| testcase_01 | AC | 18 ms
18,944 KB |
| testcase_02 | AC | 17 ms
18,816 KB |
| testcase_03 | AC | 17 ms
18,944 KB |
| testcase_04 | AC | 18 ms
18,944 KB |
| testcase_05 | AC | 17 ms
18,944 KB |
| testcase_06 | AC | 17 ms
18,816 KB |
| testcase_07 | AC | 18 ms
18,944 KB |
| testcase_08 | AC | 17 ms
18,940 KB |
| testcase_09 | AC | 17 ms
18,808 KB |
| testcase_10 | AC | 17 ms
18,844 KB |
| testcase_11 | AC | 17 ms
18,816 KB |
| testcase_12 | AC | 29 ms
20,124 KB |
| testcase_13 | AC | 62 ms
23,196 KB |
| testcase_14 | AC | 23 ms
19,712 KB |
| testcase_15 | AC | 18 ms
19,168 KB |
| testcase_16 | AC | 20 ms
19,424 KB |
| testcase_17 | AC | 18 ms
18,944 KB |
| testcase_18 | AC | 17 ms
18,944 KB |
| testcase_19 | AC | 17 ms
18,944 KB |
| testcase_20 | AC | 19 ms
19,072 KB |
| testcase_21 | AC | 32 ms
20,448 KB |
| testcase_22 | AC | 23 ms
19,584 KB |
| testcase_23 | AC | 20 ms
19,328 KB |
| testcase_24 | AC | 29 ms
20,140 KB |
| testcase_25 | AC | 18 ms
18,896 KB |
| testcase_26 | AC | 18 ms
19,200 KB |
| testcase_27 | AC | 32 ms
20,564 KB |
| testcase_28 | AC | 33 ms
20,700 KB |
| testcase_29 | AC | 32 ms
20,592 KB |
| testcase_30 | AC | 17 ms
19,048 KB |
| testcase_31 | AC | 45 ms
21,932 KB |
| testcase_32 | AC | 30 ms
20,496 KB |
| testcase_33 | AC | 20 ms
19,072 KB |
| testcase_34 | AC | 17 ms
18,944 KB |
| testcase_35 | AC | 17 ms
18,940 KB |
| testcase_36 | AC | 72 ms
24,620 KB |
| testcase_37 | AC | 45 ms
21,780 KB |
| testcase_38 | AC | 44 ms
21,776 KB |
| testcase_39 | AC | 43 ms
21,776 KB |
| testcase_40 | AC | 44 ms
21,772 KB |
| testcase_41 | AC | 44 ms
21,772 KB |
| testcase_42 | AC | 17 ms
18,816 KB |
| testcase_43 | AC | 31 ms
20,368 KB |
| testcase_44 | AC | 20 ms
19,120 KB |
| testcase_45 | AC | 17 ms
18,904 KB |
| testcase_46 | AC | 17 ms
18,944 KB |
ソースコード
#line 2 "cpplib/util/template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#include<bits/stdc++.h>
using namespace std;
struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}}__INIT__;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define endl ('\n')
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>using V=vector<T>;
template<typename T>using VV=V<V<T>>;
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<<i;f=1;}cerr<<endl;}
template<typename T>inline void debug2(T t){for(auto i:t)output(i);}
#define loop(n) for(long long _=0;_<(long long)(n);++_)
#define rep(i,...) for(auto i:range(__VA_ARGS__))
#define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
inline vector<long long> range(long long n){if(n<=0)return vector<long long>();vector<long long>v(n);iota(v.begin(),v.end(),0LL);return v;}
inline vector<long long> range(long long a,long long b){if(b<=a)return vector<long long>();vector<long long>v(b-a);iota(v.begin(),v.end(),a);return v;}
inline vector<long long> range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector<long long>();vector<long long>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
template<typename T>inline T reversed(T v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
template<typename T,typename E>bool chmin(T& s,const E& t){bool res=s>t;s=min<T>(s,t);return res;}
template<typename T,typename E>bool chmax(T& s,const E& t){bool res=s<t;s=max<T>(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
#define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__}))
vector<vector<long long>> __MAKE_MAT__(vector<long long> v){if(v.empty())return vector<vector<long long>>(1,vector<long long>());long long n=v.back();v.pop_back();vector<vector<long long>> ret;vector<vector<long long>> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i<n;++i){ret.push_back(e);ret.back().push_back(i);}return ret;}
using graph=vector<vector<int>>;
template<typename T>using graph_w=vector<vector<pair<int,T>>>;
template<typename T,typename E>ostream& operator<<(ostream& out,pair<T,E>v){out<<"("<<v.first<<","<<v.second<<")";return out;}
#line 6 "cpplib/math/FPS_base.hpp"
#include<type_traits>
#line 8 "cpplib/math/FPS_base.hpp"
/**
* @brief 形式的冪級数(BASE)
*/
template<typename T,typename F>
struct FPS_BASE:std::vector<T>{
using std::vector<T>::vector;
using P=FPS_BASE<T,F>;
F fft;
FPS_BASE(){}
inline P operator +(T x)const noexcept{return P(*this)+=x;}
inline P operator -(T x)const noexcept{return P(*this)-=x;}
inline P operator *(T x)const noexcept{return P(*this)*=x;}
inline P operator /(T x)const noexcept{return P(*this)/=x;}
inline P operator <<(int x)noexcept{return P(*this)<<=x;}
inline P operator >>(int x)noexcept{return P(*this)>>=x;}
inline P operator +(const P& x)const noexcept{return P(*this)+=x;}
inline P operator -(const P& x)const noexcept{return P(*this)-=x;}
inline P operator -()const noexcept{return P(1,T(0))-=P(*this);}
inline P operator *(const P& x)const noexcept{return P(*this)*=x;}
inline P operator /(const P& x)const noexcept{return P(*this)/=x;}
inline P operator %(const P& x)const noexcept{return P(*this)%=x;}
bool operator ==(P x){
for(int i=0;i<(int)max((*this).size(),x.size());++i){
if(i>=(int)(*this).size()&&x[i]!=T())return 0;
if(i>=(int)x.size()&&(*this)[i]!=T())return 0;
if(i<(int)min((*this).size(),x.size()))if((*this)[i]!=x[i])return 0;
}
return 1;
}
P &operator +=(T x){
if(this->size()==0)this->resize(1,T(0));
(*this)[0]+=x;
return (*this);
}
P &operator -=(T x){
if(this->size()==0)this->resize(1,T(0));
(*this)[0]-=x;
return (*this);
}
P &operator *=(T x){
for(int i=0;i<(int)this->size();++i){
(*this)[i]*=x;
}
return (*this);
}
P &operator /=(T x){
if(std::is_same<T,long long>::value){
for(int i=0;i<(int)this->size();++i){
(*this)[i]/=x;
}
return (*this);
}
return (*this)*=(T(1)/x);
}
P &operator <<=(int x){
P ret(x,T(0));
ret.insert(ret.end(),begin(*this),end(*this));
return (*this)=ret;
}
P &operator >>=(int x){
if((int)(*this).size()<=x)return (*this)=P();
P ret;
ret.insert(ret.end(),begin(*this)+x,end(*this));
return (*this)=ret;
}
P &operator +=(const P& x){
if(this->size()<x.size())this->resize(x.size(),T(0));
for(int i=0;i<(int)x.size();++i){
(*this)[i]+=x[i];
}
return (*this);
}
P &operator -=(const P& x){
if(this->size()<x.size())this->resize(x.size(),T(0));
for(int i=0;i<(int)x.size();++i){
(*this)[i]-=x[i];
}
return (*this);
}
P &operator *=(const P& x){
return (*this)=F()(*this,x);
}
P &operator /=(P x){
if(this->size()<x.size()) {
this->clear();
return (*this);
}
const int n=this->size()-x.size()+1;
return (*this) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n);
}
P &operator %=(const P& x){
return ((*this)-=(*this)/x*x);
}
inline void print(){
for(int i=0;i<(int)(*this).size();++i)std::cerr<<(*this)[i]<<" \n"[i==(int)(*this).size()-1];
if((int)(*this).size()==0)std::cerr<<'\n';
}
inline P& shrink(){while((*this).back()==0)(*this).pop_back();return (*this);}
inline P pre(int sz)const{
return P(begin(*this),begin(*this)+std::min((int)this->size(),sz));
}
P rev(int deg=-1){
P ret(*this);
if(deg!=-1)ret.resize(deg,T(0));
reverse(begin(ret),end(ret));
return ret;
}
P inv(int deg=-1){
assert((*this)[0]!=T(0));
const int n=deg==-1?this->size():deg;
P ret({T(1)/(*this)[0]});
for(int i=1;i<n;i<<=1){
ret*=(-ret*pre(i<<1)+2).pre(i<<1);
}
return ret.pre(n);
}
inline P dot(const P& x){
P ret(*this);
for(int i=0;i<int(min(this->size(),x.size()));++i){
ret[i]*=x[i];
}
return ret;
}
P diff(){
if((int)(*this).size()<=1)return P();
P ret(*this);
for(int i=0;i<(int)ret.size();i++){
ret[i]*=i;
}
return ret>>1;
}
P integral(){
P ret(*this);
for(int i=0;i<(int)ret.size();i++){
ret[i]/=i+1;
}
return ret<<1;
}
P log(int deg=-1){
assert((*this)[0]==T(1));
const int n=deg==-1?this->size():deg;
return (diff()*inv(n)).pre(n-1).integral();
}
P exp(int deg=-1){
assert((*this)[0]==T(0));
const int n=deg==-1?this->size():deg;
P ret({T(1)});
for(int i=1;i<n;i<<=1){
ret=ret*(pre(i<<1)+1-ret.log(i<<1)).pre(i<<1);
}
return ret.pre(n);
}
P pow(int c,int deg=-1){
const int n=deg==-1?this->size():deg;
long long i=0;
P ret(*static_cast<P*>(this));
while(i!=(int)this->size()&&ret[i]==0)i++;
if(i==(int)this->size())return P(n,0);
if(i*c>=n)return P(n,0);
T k=ret[i];
return ((((ret>>i)/k).log()*c).exp()*(k.pow(c))<<(i*c)).pre(n);
// const int n=deg==-1?this->size():deg;
// long long i=0;
// P ret(*this);
// while(i!=(int)this->size()&&ret[i]==0)i++;
// if(i==(int)this->size())return P(n,0);
// if(i*c>=n)return P(n,0);
// T k=ret[i];
// return ((((ret>>i)/k).log()*c).exp()*(k.pow(c))<<(i*c)).pre(n);
// P x(*this);
// P ret(1,1);
// while(c) {
// if(c&1){
// ret*=x;
// if(~deg)ret=ret.pre(deg);
// }
// x*=x;
// if(~deg)x=x.pre(deg);
// c>>=1;
// }
// return ret;
}
P sqrt(int deg=-1){
const int n=deg==-1?this->size():deg;
if((*this)[0]==T(0)) {
for(int i=1;i<(int)this->size();i++) {
if((*this)[i]!=T(0)) {
if(i&1)return{};
if(n-i/2<=0)break;
auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
if((int)ret.size()<n)ret.resize(n,T(0));
return ret;
}
}
return P(n,0);
}
P ret({T(1)});
for(int i=1;i<n;i<<=1){
ret=(ret+pre(i<<1)*ret.inv(i<<1)).pre(i<<1)/T(2);
}
return ret.pre(n);
}
P shift(int c){
const int n=this->size();
P f(*this),g(n,0);
for(int i=0;i<n;++i)f[i]*=F().fact(T(i));
for(int i=0;i<n;++i)g[i]=F().pow(T(c),i)/F().fact(T(i));
g=g.rev();
f*=g;
f>>=n-1;
for(int i=0;i<n;++i)f[i]/=F().fact(T(i));
return f;
}
T eval(T x){
T res=0;
for(int i=(int)this->size()-1;i>=0;--i){
res*=x;
res+=(*this)[i];
}
return res;
}
static P interpolation(const std::vector<T>&x,const std::vector<T>& y){
const int n=x.size();
std::vector<std::pair<P,P>>a(n*2-1);
std::vector<P> b(n*2-1);
for(int i=0;i<n;++i)a[i+n-1]=std::make_pair(P{1},P{T()-x[i],1});
for(int i=n-2;i>=0;--i)a[i]={a[2*i+1].first*a[2*i+2].second+a[2*i+2].first*a[2*i+1].second,a[2*i+1].second*a[2*i+2].second};
auto d=(a[0].first).multipoint_eval(x);
for(int i=0;i<n;++i)b[i+n-1]=P{T(y[i]/d[i])};
for(int i=n-2;i>=0;--i)b[i]=b[2*i+1]*a[2*i+2].second+b[2*i+2]*a[2*i+1].second;
return b[0];
}
static P interpolation(const std::vector<T>& y){
const int n=y.size();
std::vector<std::pair<P,P>>a(n*2-1);
std::vector<P>b(n*2-1);
for(int i=0;i<n;++i)a[i+n-1]=std::make_pair(P{1},P{T()-i,1});
for(int i=n-2;i>=0;--i)a[i]={a[2*i+1].first*a[2*i+2].second+a[2*i+2].first*a[2*i+1].second,a[2*i+1].second*a[2*i+2].second};
for(int i=0;i<n;++i){
T tmp=F().fact(T(i))*F().pow(T(-1),i)*F().fact(T(n-1-i));
b[i+n-1]=P{T(y[i]/tmp)};
}
for(int i=n-2;i>=0;--i)b[i]=b[2*i+1]*a[2*i+2].second+b[2*i+2]*a[2*i+1].second;
return b[0];
}
std::vector<T> multipoint_eval(const std::vector<T>&x){
const int n=x.size();
P* v=new P[2*n-1];
for(int i=0;i<n;i++)v[i+n-1]={T()-x[i],T(1)};
for(int i=n-2;i>=0;i--){v[i]=v[i*2+1]*v[i*2+2];}
v[0]=P(*this)%v[0];v[0].shrink();
for(int i=1;i<n*2-1;i++){
v[i]=v[(i-1)/2]%v[i];
v[i].shrink();
}
std::vector<T>res(n);
for(int i=0;i<n;i++)res[i]=v[i+n-1][0];
return res;
}
P slice(int s,int e,int k){
P res;
for(int i=s;i<e;i+=k)res.push_back((*this)[i]);
return res;
}
T nth_term(P q,int64_t x){
if(x==0)return (*this)[0]/q[0];
P p(*this);
P q2=q;
for(int i=1;i<(int)q2.size();i+=2)q2[i]*=-1;
q*=q2;
p*=q2;
return p.slice(x%2,p.size(),2).nth_term(q.slice(0,q.size(),2),x/2);
}
//(*this)(t(x))
P manipulate(P t,int deg){
P s=P(*this);
if(deg==0)return P();
if((int)t.size()==1)return P{s.eval(t[0])};
int k=std::min((int)::sqrt(deg/(::log2(deg)+1))+1,(int)t.size());
int b=deg/k+1;
P t2=t.pre(k);
std::vector<P>table(s.size()/2+1,P{1});
for(int i=1;i<(int)table.size();i++){
table[i]=((table[i-1])*t2).pre(deg);
}
auto f=[&](auto f,auto l,auto r,int deg)->P{
if(r-l==1)return P{*l};
auto m=l+(r-l)/2;
return f(f,l,m,deg)+(table[m-l]*f(f,m,r,deg)).pre(deg);
};
P ans=P();
P tmp=f(f,s.begin(),s.end(),deg);
P tmp2=P{1};
T tmp3=T(1);
int tmp5=-1;
P tmp6=t2.diff();
if(tmp6==P()){
for(int i=0;i<b;++i){
if(tmp.size()==0)break;
ans+=(tmp2*tmp[0]).pre(deg)/tmp3;
tmp=tmp.diff();
tmp2=(tmp2*(t-t2)).pre(deg);
tmp3*=T(i+1);
}
}else{
while(t2[++tmp5]==T());
P tmp4=(tmp6>>(tmp5-1)).inv(deg);
for(int i=0;i<b;++i){
ans+=(tmp*tmp2).pre(deg)/tmp3;
tmp=((tmp.diff()>>(tmp5-1))*tmp4).pre(deg);
tmp2=(tmp2*(t-t2)).pre(deg);
tmp3*=T(i+1);
}
}
return ans;
}
//(*this)(t(x))
P manipulate2(P t,int deg){
P ans=P();
P s=(*this).rev();
for(int i=0;i<(int)s.size();++i){
ans=(ans*t+s[i]).pre(deg);
}
return ans;
}
P find_linear_recurrence()const{
const int n=this->size();
P b={T(-1)},c={T(-1)};
T y=T(1);
for(int i=1;i<=n;++i){
int l=c.size(),m=b.size();
T x=0;
for(int j=0;j<l;++j)x+=c[j]*(*this)[i-l+j];
b.emplace_back(0);
m++;
if(x==T(0))continue;
T freq=x/y;
if(l<m){
auto tmp=c;
c<<=m-l;
c-=b*freq;
b=tmp;
y=x;
}else{
c-=(b*freq)<<(l-m);
}
}
return c;
}
static P stirling_second(int n){
P a(n+1,0),b(n+1,0);
for(int i=0;i<=n;++i){
a[i]=F().pow(T(i),n)/F().fact(T(i));
b[i]=(i%2?T(-1):T(1))/F().fact(T(i));
}
return (a*b).pre(n+1);
}
void debug(){
for(int i=0;i<(int)(*this).size();++i)std::cerr<<(*this)[i]<<" \n"[i==(int)(*this).size()-1];
}
};
#line 3 "cpplib/math/FPS_mint.hpp"
//#include"../util/ACL.hpp"
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <utility>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i <= cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
#line 1 "cpplib/math/ceil_pow2.hpp"
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
#line 1 "cpplib/math/mod_pow.hpp"
/**
* @brief (x^y)%mod
*/
long long mod_pow(long long x,long long y,long long mod){
long long ret=1;
while(y>0) {
if(y&1)(ret*=x)%=mod;
(x*=x)%=mod;
y>>=1;
}
return ret;
}
#line 4 "cpplib/math/garner.hpp"
/**
*
* @brief ガーナーのアルゴリズム
*
*/
long long garner(std::vector<long long>a,std::vector<long long>mods){
const int sz=3;
long long coeffs[sz+1]={1,1,1,1};
long long constants[sz+1]={};
for(int i=0;i<sz;i++){
long long v=(mods[i]+a[i]-constants[i])%mods[i]*mod_pow(coeffs[i],mods[i]-2,mods[i])%mods[i];
for(int j=i+1;j<sz+1;j++) {
constants[j]=(constants[j]+coeffs[j]*v)%mods[j];
coeffs[j]=(coeffs[j]*mods[i])%mods[j];
}
}
return constants[3];
}
#line 7 "cpplib/math/FPS_mint.hpp"
/**
* @brief 形式的冪級数(ModInt)
*/
template<typename Mint>
struct _FPS{
template<typename T>
T operator()(const T& _s,const T& _t){
if(_s.size()==0||_t.size()==0)return T();
const size_t sz=_s.size()+_t.size()-1;
if((Mint::get_mod()&((1<<ceil_pow2(sz))-1))==1){
std::vector<atcoder::static_modint<Mint::get_mod()>>s(_s.size()),t(_t.size());
for(size_t i=0;i<_s.size();++i)s[i]=_s[i].value();
for(size_t i=0;i<_t.size();++i)t[i]=_t[i].value();
std::vector<atcoder::static_modint<Mint::get_mod()>> _v=atcoder::convolution(s,t);
T v(_v.size());
for (size_t i=0;i<_v.size();++i)v[i]=_v[i].val();
return v;
}else{
std::vector<atcoder::static_modint<1224736769>>s1(_s.size()),t1(_t.size());
std::vector<atcoder::static_modint<1045430273>>s2(_s.size()),t2(_t.size());
std::vector<atcoder::static_modint<1007681537>>s3(_s.size()),t3(_t.size());
for(size_t i=0;i<_s.size();++i){
s1[i]=_s[i].value();
s2[i]=_s[i].value();
s3[i]=_s[i].value();
}
for(size_t i=0;i<_t.size();++i){
t1[i]=_t[i].value();
t2[i]=_t[i].value();
t3[i]=_t[i].value();
}
auto v1=atcoder::convolution(s1,t1);
auto v2=atcoder::convolution(s2,t2);
auto v3=atcoder::convolution(s3,t3);
T v(sz);
for(size_t i=0;i<sz;++i){
v[i]=garner(std::vector<long long>{v1[i].val(),v2[i].val(),v3[i].val()},std::vector<long long>{1224736769,1045430273,1007681537,Mint::get_mod()});
}
return v;
}
}
template<typename T>
T fact(const T& s){
return s.fact();
}
template<typename T>
T pow(const T& s,long long i){
return s.pow(i);
}
};
template<typename Mint>using fps=FPS_BASE<Mint,_FPS<Mint>>;
#line 5 "cpplib/math/mod_int.hpp"
/**
* @brief ModInt
*/
template<int MOD>
struct mod_int {
using mint=mod_int<MOD>;
using u64 = std::uint_fast64_t;
u64 a;
constexpr mod_int(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){}
constexpr u64 &value()noexcept{return a;}
constexpr const u64 &value() const noexcept {return a;}
constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;}
constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;}
constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;}
constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;}
constexpr mint &operator+=(const mint rhs) noexcept {
a += rhs.a;
if (a >= get_mod())a -= get_mod();
return *this;
}
constexpr mint &operator-=(const mint rhs) noexcept {
if (a<rhs.a)a += get_mod();
a -= rhs.a;
return *this;
}
constexpr mint &operator*=(const mint rhs) noexcept {
a = a * rhs.a % get_mod();
return *this;
}
constexpr mint operator++(int) noexcept {
a += 1;
if (a >= get_mod())a -= get_mod();
return *this;
}
constexpr mint operator--(int) noexcept {
if (a<1)a += get_mod();
a -= 1;
return *this;
}
constexpr mint &operator/=(mint rhs) noexcept {
u64 exp=get_mod()-2;
while (exp) {
if (exp % 2) {
*this *= rhs;
}
rhs *= rhs;
exp /= 2;
}
return *this;
}
constexpr bool operator==(mint x) noexcept {
return a==x.a;
}
constexpr bool operator!=(mint x) noexcept {
return a!=x.a;
}
constexpr bool operator<(mint x) noexcept {
return a<x.a;
}
constexpr bool operator>(mint x) noexcept {
return a>x.a;
}
constexpr bool operator<=(mint x) noexcept {
return a<=x.a;
}
constexpr bool operator>=(mint x) noexcept {
return a>=x.a;
}
constexpr static int root(){
mint root = 2;
while(root.pow((get_mod()-1)>>1).a==1)root++;
return root.a;
}
constexpr mint pow(long long n)const{
long long x=a;
mint ret = 1;
while(n>0) {
if(n&1)(ret*=x);
(x*=x)%=get_mod();
n>>=1;
}
return ret;
}
constexpr mint inv(){
return pow(get_mod()-2);
}
static std::vector<mint> fac;
static std::vector<mint> ifac;
static bool init;
constexpr static int mx=1000001;
void build()const{
init=0;
fac.resize(mx);
ifac.resize(mx);
fac[0]=1,ifac[0]=1;
for(int i=1;i<mx;i++)fac[i]=fac[i-1]*i;
ifac[mx-1]=fac[mx-1].inv();
for(int i=mx-2;i>=0;i--)ifac[i]=ifac[i+1]*(i+1);
}
mint comb(long long b){
if(init)build();
if(a==0&&b==0)return 1;
if((long long)a<b)return 0;
return fac[a]*ifac[a-b]*ifac[b];
}
mint fact()const{
if(init)build();
return fac[a];
}
mint fact_inv()const{
if(init)build();
return ifac[a];
}
friend std::ostream& operator<<(std::ostream& lhs, const mint& rhs) noexcept {
lhs << rhs.a;
return lhs;
}
friend std::istream& operator>>(std::istream& lhs,mint& rhs) noexcept {
lhs >> rhs.a;
return lhs;
}
constexpr static u64 get_mod(){
return MOD;
}
};
template<int MOD>std::vector<mod_int<MOD>> mod_int<MOD>::fac;
template<int MOD>std::vector<mod_int<MOD>> mod_int<MOD>::ifac;
template<int MOD>bool mod_int<MOD>::init=1;
#line 3 "cpplib/math/mod_int998244353.hpp"
using mint=mod_int<998'244'353>;
/**
* @brief ModInt(998'244'353)
*/
#line 4 "code.cpp"
int main(){
lint n,m,k;
cin>>n>>m>>k;
// vector<mint>ans(k+1);
// rep(i,k+1){
// ans[i]=mint(m+i).pow(n);
// rep(j,i){
// ans[i]-=ans[j]*mint(i).comb(j);
// }
// }
// cout<<ans[k]*mint(m).comb(k)<<endl;
fps<mint>ans(k+1),tmp(k+1);
rep(i,k+1){
ans[i]=mint(m+i).pow(n)/mint(i).fact();
tmp[i]=mint(i).fact_inv()*mint(-1).pow(i);
}
ans*=tmp;
cout<<ans[k]*mint(k).fact()*mint(m).comb(k)<<endl;
}