#543328 (C++17) No.1204 お菓子配り-FINAL

• 問題: No.1204 お菓子配り-FINAL
• ユーザー: maroon_kuri
• 提出日時: 2020-08-30 01:45:24
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 253 ms / 8,000 ms
• コード長: 9,972 bytes
• コンパイル時間: 2,761 ms
• コンパイル使用メモリ: 214,116 KB
• 実行使用メモリ: 69,248 KB
• 最終ジャッジ日時: 2024-11-14 17:48:29
• 合計ジャッジ時間: 15,273 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	51 ms; 68,992 KB
testcase_01	AC	77 ms; 68,988 KB
testcase_02	AC	48 ms; 69,120 KB
testcase_03	AC	49 ms; 68,984 KB
testcase_04	AC	47 ms; 69,116 KB
testcase_05	AC	59 ms; 69,116 KB
testcase_06	AC	55 ms; 68,992 KB
testcase_07	AC	79 ms; 69,120 KB
testcase_08	AC	44 ms; 69,116 KB
testcase_09	AC	53 ms; 68,988 KB
testcase_10	AC	55 ms; 69,240 KB
testcase_11	AC	47 ms; 68,984 KB
testcase_12	AC	63 ms; 68,988 KB
testcase_13	AC	54 ms; 69,116 KB
testcase_14	AC	57 ms; 69,116 KB
testcase_15	AC	47 ms; 68,988 KB
testcase_16	AC	52 ms; 69,116 KB
testcase_17	AC	44 ms; 68,992 KB
testcase_18	AC	47 ms; 69,112 KB
testcase_19	AC	47 ms; 69,116 KB
testcase_20	AC	51 ms; 68,992 KB
testcase_21	AC	85 ms; 69,116 KB
testcase_22	AC	57 ms; 68,984 KB
testcase_23	AC	83 ms; 68,988 KB
testcase_24	AC	69 ms; 69,120 KB
testcase_25	AC	43 ms; 68,992 KB
testcase_26	AC	59 ms; 68,992 KB
testcase_27	AC	80 ms; 68,984 KB
testcase_28	AC	42 ms; 69,116 KB
testcase_29	AC	76 ms; 69,116 KB
testcase_30	AC	65 ms; 69,116 KB
testcase_31	AC	80 ms; 68,984 KB
testcase_32	AC	48 ms; 68,984 KB
testcase_33	AC	58 ms; 68,988 KB
testcase_34	AC	47 ms; 69,112 KB
testcase_35	AC	59 ms; 69,112 KB
testcase_36	AC	63 ms; 68,992 KB
testcase_37	AC	60 ms; 69,116 KB
testcase_38	AC	47 ms; 69,116 KB
testcase_39	AC	52 ms; 68,984 KB
testcase_40	AC	69 ms; 68,988 KB
testcase_41	AC	44 ms; 69,120 KB
testcase_42	AC	43 ms; 69,116 KB
testcase_43	AC	44 ms; 68,984 KB
testcase_44	AC	44 ms; 68,988 KB
testcase_45	AC	44 ms; 68,988 KB
testcase_46	AC	44 ms; 69,116 KB
testcase_47	AC	45 ms; 69,116 KB
testcase_48	AC	68 ms; 69,116 KB
testcase_49	AC	73 ms; 68,992 KB
testcase_50	AC	63 ms; 69,116 KB
testcase_51	AC	46 ms; 69,116 KB
testcase_52	AC	44 ms; 68,988 KB
testcase_53	AC	62 ms; 68,992 KB
testcase_54	AC	55 ms; 69,248 KB
testcase_55	AC	46 ms; 68,984 KB
testcase_56	AC	68 ms; 69,116 KB
testcase_57	AC	43 ms; 68,992 KB
testcase_58	AC	48 ms; 69,120 KB
testcase_59	AC	50 ms; 68,992 KB
testcase_60	AC	42 ms; 69,112 KB
testcase_61	AC	42 ms; 68,988 KB
testcase_62	AC	42 ms; 68,988 KB
testcase_63	AC	42 ms; 69,116 KB
testcase_64	AC	43 ms; 69,116 KB
testcase_65	AC	43 ms; 68,988 KB
testcase_66	AC	44 ms; 69,120 KB
testcase_67	AC	44 ms; 69,116 KB
testcase_68	AC	43 ms; 68,992 KB
testcase_69	AC	41 ms; 68,988 KB
testcase_70	AC	43 ms; 68,992 KB
testcase_71	AC	42 ms; 69,120 KB
testcase_72	AC	42 ms; 69,116 KB
testcase_73	AC	43 ms; 68,988 KB
testcase_74	AC	42 ms; 68,988 KB
testcase_75	AC	43 ms; 69,120 KB
testcase_76	AC	43 ms; 68,992 KB
testcase_77	AC	42 ms; 69,116 KB
testcase_78	AC	42 ms; 69,116 KB
testcase_79	AC	41 ms; 68,988 KB
testcase_80	AC	42 ms; 68,984 KB
testcase_81	AC	43 ms; 69,116 KB
testcase_82	AC	43 ms; 69,116 KB
testcase_83	AC	43 ms; 69,112 KB
testcase_84	AC	42 ms; 68,988 KB
testcase_85	AC	42 ms; 68,992 KB
testcase_86	AC	42 ms; 68,992 KB
testcase_87	AC	42 ms; 68,988 KB
testcase_88	AC	40 ms; 69,112 KB
testcase_89	AC	42 ms; 69,112 KB
testcase_90	AC	127 ms; 68,988 KB
testcase_91	AC	67 ms; 68,988 KB
testcase_92	AC	85 ms; 69,112 KB
testcase_93	AC	148 ms; 69,244 KB
testcase_94	AC	123 ms; 69,120 KB
testcase_95	AC	158 ms; 69,116 KB
testcase_96	AC	253 ms; 68,988 KB
testcase_97	AC	61 ms; 68,988 KB
testcase_98	AC	128 ms; 68,988 KB
testcase_99	AC	160 ms; 68,988 KB
testcase_100	AC	48 ms; 68,988 KB
testcase_101	AC	125 ms; 68,988 KB
testcase_102	AC	199 ms; 68,988 KB
testcase_103	AC	184 ms; 68,988 KB
testcase_104	AC	227 ms; 69,116 KB
testcase_105	AC	57 ms; 68,988 KB
testcase_106	AC	43 ms; 68,984 KB
testcase_107	AC	52 ms; 69,116 KB
testcase_108	AC	132 ms; 68,988 KB
testcase_109	AC	153 ms; 69,112 KB
testcase_110	AC	101 ms; 68,988 KB
testcase_111	AC	92 ms; 69,120 KB
testcase_112	AC	95 ms; 68,984 KB
testcase_113	AC	97 ms; 69,120 KB
testcase_114	AC	98 ms; 68,988 KB
testcase_115	AC	98 ms; 69,116 KB
testcase_116	AC	101 ms; 69,120 KB
testcase_117	AC	98 ms; 68,988 KB
testcase_118	AC	91 ms; 69,116 KB
testcase_119	AC	105 ms; 68,988 KB
testcase_120	AC	112 ms; 68,992 KB
testcase_121	AC	92 ms; 68,988 KB
testcase_122	AC	101 ms; 69,112 KB
testcase_123	AC	90 ms; 68,988 KB
testcase_124	AC	110 ms; 68,988 KB
testcase_125	AC	107 ms; 68,992 KB
testcase_126	AC	99 ms; 69,120 KB
testcase_127	AC	100 ms; 69,116 KB
testcase_128	AC	99 ms; 69,116 KB
testcase_129	AC	134 ms; 69,116 KB

ソースコード

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

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif
	return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

struct modinfo{uint mod,root;};
template<modinfo const&ref>
struct modular{
	static constexpr uint const &mod=ref.mod;
	static modular root(){return modular(ref.root);}
	uint v;
	//modular(initializer_list<uint>ls):v(*ls.bg){}
	modular(ll vv=0){s(vv%mod+mod);}
	modular& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	modular operator-()const{return modular()-*this;}
	modular& operator+=(const modular&rhs){return s(v+rhs.v);}
	modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
	modular&operator*=(const modular&rhs){
		v=ull(v)*rhs.v%mod;
		return *this;
	}
	modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
	modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
	modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
	modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
	modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
	modular pow(int n)const{
		modular res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	modular inv()const{return pow(mod-2);}
	/*modular inv()const{
		int x,y;
		int g=extgcd<ll>(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return modular(x);
	}*/
	friend modular operator+(int x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(int x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(int x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(int x,const modular&y){
		return modular(x)/y;
	}
	friend ostream& operator<<(ostream&os,const modular&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,modular&m){
		ll x;is>>x;
		m=modular(x);
		return is;
	}
	bool operator<(const modular&r)const{return v<r.v;}
	bool operator==(const modular&r)const{return v==r.v;}
	bool operator!=(const modular&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};

//extern constexpr modinfo base{998244353,3};
extern constexpr modinfo base{1000000007,0};
//modinfo base{1,0};
using mint=modular<base>;

const int vmax=(1<<21)+10;
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
	fact[0]=1;
	rng(i,1,vmax){
		fact[i]=fact[i-1]*i;
	}
	finv[vmax-1]=fact[vmax-1].inv();
	for(int i=vmax-2;i>=0;i--){
		finv[i]=finv[i+1]*(i+1);
	}
	for(int i=vmax-1;i>=1;i--){
		invs[i]=finv[i]*fact[i-1];
	}
}
mint choose(int n,int k){
	return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
	return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
	return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}

/*
const int vmax=110;
mint binbuf[vmax][vmax];
mint choose(int n,int k){
	return binbuf[n-k][k];
}
mint binom(int a,int b){
	return binbuf[a][b];
}
void initfact(){
	binbuf[0][0]=1;
	rep(i,vmax)rep(j,vmax){
		if(i)binbuf[i][j]+=binbuf[i-1][j];
		if(j)binbuf[i][j]+=binbuf[i][j-1];
	}
}
*/

const int mmax=105;
const int nmax=100005;

mint small[mmax];
mint pbuf[mmax][nmax];
int off,xmax,pmax;
mint getpow(int x,int p){
	assert(inc(off,x,xmax));
	assert(inc(0,p,pmax));
	return pbuf[x-off][p];
};

mint sub(int n,int k){
	assert(k<=n);
	if(k==0)return 1;
	return getpow(n,k-1)*(n-k);
}

mint slv1(int a,int n,int k){
	assert(a>=0);
	assert(inc(a,k,n-1));
	mint res=sub(n,k);
	rng(i,1,min(a,k+1)+1)
		res-=choose(k,i-1)*small[i]*sub(n-i,k-(i-1));
	return res;
}

mint slv2(int a,int n,int k){
	assert(a>=0);
	assert(inc(a,k,n));
	if(a==0)return getpow(n,k);
	else{
		mint res=slv2(a-1,n,k);
		if(k<n)res-=slv1(a-1,n,k);
		return res;
	}
}

mint slv5(int a,int n,int k){
	assert(a>=0);
	assert(inc(a,k,n));
	mint res=getpow(n,k);
	if(a>=1)res-=sub(n,k)*a;
	if(a>=2&&k<=n-2){
		rep(i,min(a-2,k)+1){
			res+=sub(n-(i+1),k-i)*(a-1-i)*small[i+1]*choose(k,i);
		}
	}
	return res;
}

mint slv3(int a,int b,int n,int k){
	assert(a>=0);
	assert(b>=0);
	assert(a+b+1<=n);
	assert(inc(a+b,k,n-1));
	if(a==0)return slv1(b,n,k);
	else{
		mint res=slv3(a-1,b,n,k);
		if(k>=a-1&&k<=n-2)res-=choose(k,a-1)*small[a]*slv1(b,n-a,k-(a-1));
		return res;
	}
}

mint conv[mmax];

mint slv4(int a,int b,int n,int k){
	assert(a>=0);
	assert(b>=0);
	assert(a+b+1<=n);
	assert(inc(a+b,k,n-1));
	mint res=sub(n,k);
	if(k<=n-2){
		rep(_,2){
			rng(i,1,min(a,k+1)+1){
				res-=choose(k,i-1)*small[i]*sub(n-i,k-(i-1));
			}
			swap(a,b);
		}
	}
	if(k<=n-3){
		rep(sum,min(k+1,a+b-1)){
			res+=choose(k,sum)*conv[sum]*sub(n-(sum+2),k-sum);
		}
	}
	return res;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	initfact();
	
	int n,m;cin>>n>>m;
	off=n-m;
	xmax=n;
	pmax=n;
	rng(v,n-m,n+1){
		int idx=v-off;
		pbuf[idx][0]=1;
		rep(i,n)pbuf[idx][i+1]=pbuf[idx][i]*v;
	}
	small[1]=1;
	rng(i,2,m+2){
		small[i]=mint(i).pow(i-2);
	}
	
	vi ls;
	int cur=0;
	string s;cin>>s;
	int cnt=0;
	for(auto c:s){
		if(c=='o'){
			ls.pb(cur);
			cur=0;
		}else{
			cnt++;
			cur++;
		}
	}
	ls.pb(cur);
	mint ans;
	if(si(ls)==1){
		rng(k,cnt,n+1){
			mint ad=slv5(ls[0],n,k)*getpow(n,n-k);
			#ifdef LOCAL
			{
				mint tmp=slv2(ls[0],n,k)*getpow(n,n-k);
				assert(ad==tmp);
			}
			#endif
			ans+=ad;
		}
	}else{
		int a=ls[0],b=ls.back();
		rep(i,a)rep(j,b){
			conv[i+j]+=small[i+1]*small[j+1]*binom(i,j);
		}
		mint w=1;
		int u=0;
		rng(i,1,si(ls)-1){
			w*=small[ls[i]+1];
			w*=finv[ls[i]];
			u+=ls[i];
		}
		w*=fact[u];
		rng(k,cnt,n-(si(ls)-1)+1){
			mint ad=slv4(a,b,n-(si(ls)-2)-u,k-u)*choose(k,u)*getpow(n,n-k);
			#ifdef LOCAL
			{
				mint tmp=slv3(ls[0],ls.back(),n-(si(ls)-2)-u,k-u)*choose(k,u)*getpow(n,n-k);
				assert(tmp==ad);
			}
			#endif
			ans+=ad;
		}
		ans*=w;
	}
	print(ans*(n-m+1));
}