1 #include<algorithm>
2 #include<iostream>
3 #include<cstdlib>
4 #include<cstring>
5 #include<cstdio>
6 #include<string>
7 #include<cmath>
8 #include<ctime>
9 #include<queue>
10 #include<stack>
11 #include<map>
12 #include<set>
13 #define rre(i,r,l) for(int i=(r);i>=(l);i--)
14 #define re(i,l,r) for(int i=(l);i<=(r);i++)
15 #define Clear(a,b) memset(a,b,sizeof(a))
16 #define inout(x) printf("%d",(x))
17 #define douin(x) scanf("%lf",&x)
18 #define strin(x) scanf("%s",(x))
19 #define LLin(x) scanf("%lld",&x)
20 #define op operator
21 #define CSC main
22 typedef unsigned long long ULL;
23 typedef const int cint;
24 typedef long long LL;
25 using namespace std;
26 void inin(int &ret)
27 {
28 ret=0;int f=0;char ch=getchar();
29 while(ch<'0'||ch>'9'){if(ch=='-')f=1;ch=getchar();}
30 while(ch>='0'&&ch<='9')ret*=10,ret+=ch-'0',ch=getchar();
31 ret=f?-ret:ret;
32 }
33 namespace C
34 {
35 int c[1010][1010];
36 void js1(int n)//????¨¨y??
37 {
38 c[1][1]=1;
39 re(i,1,n)
40 {
41 c[i][1]=i;
42 re(j,2,i)c[i][j]=c[i-1][j-1]+c[i-1][j];
43 }
44 }
45 void js2(int n,int k)//O(n)¦ÌY¨ª?
46 {
47 c[n][1]=n;
48 re(i,2,n)c[n][i]=c[n][i-1]*(n-i+1)/i;
49 }
50 }
51 namespace prime
52 {
53 int prime[100010],prime_tot;
54 bool bo[1000010];
55 void shai(int limit)//??D?¨¦?
56 {
57 re(i,2,limit)
58 {
59 if(!bo[i])prime[++prime_tot]=i;
60 for(int j=1;j<=prime_tot&&i*prime[j]<=limit;j++)
61 {
62 bo[i*prime[j]]=1;
63 if(i%prime[j]==0)break;
64 }
65 }
66 }
67 bool pd(int x)//??¨ºy?D?¡§
68 {
69 shai(sqrt(x)+1);
70 re(i,1,prime_tot)if(x%prime[i]==0)return 0;
71 return 1;
72 }
73 }
74 namespace nt
75 {
76 LL gcd(LL a,LL b){LL c;while(a%b)c=a%b,a=b,b=c;return b;}
77 void exgcd(LL a,LL b,LL &d,LL &x,LL &y)//¨¤??1?¡¤??¨¤?¦Ì?
78 {
79 if(!b){d=a;x=1,y=0;}
80 else exgcd(b,a%b,d,y,x),y-=x*(a/b);
81 }
82 LL qpow(LL a,LL b,LL mod)//?¨¬?¨´?Y
83 {
84 a%=mod;LL ret=1;
85 while(b)
86 {
87 if(b&1)ret=ret*a%mod;
88 b>>=1;
89 a=a*a%mod;
90 }
91 return ret;
92 }
93 LL PHI(LL x)
94 {
95 LL ret=x;
96 for(LL i=2;i*i<=x;i++)if(x%i==0)
97 {
98 ret=ret-ret/i;
99 while(x%i==0)x/=i;
100 }
101 if(x>1)
102 ret=ret-ret/x;
103 return ret;
104 }
105 int phi[1000010],prime[1000010],tot;
106 bool a[1000010];
107 void shai(int limit)
108 {
109 phi[1]=1;
110 re(i,2,limit)
111 {
112 if(!a[i])prime[++tot]=i;
113 for(int j=1;j<=tot&&i*prime[j]<=limit;j++)
114 {
115 a[i*prime[j]]=1;
116 if(i%prime[j]==0)
117 {
118 phi[i*prime[j]]=phi[i]*prime[j];
119 break;
120 }
121 else phi[i*prime[j]]=phi[i]*(prime[j]-1);
122 }
123 }
124 }
125 LL inv1(LL a,LL n)//???a(exgcd)
126 {
127 LL d,x,y;
128 exgcd(a,n,d,x,y);
129 return d==1?(x+n)%n:-1;
130 }
131 LL inv2(LL a,LL n)//???a(¡¤??¨ªD??¡§¨¤¨ª)
132 {
133 if(gcd(a,n)!=1)return -1;
134 LL zhi=PHI(n);
135 return qpow(a,zhi-1,n);
136 }
137 LL inv[1000010];
138 void getinv(LL mod)
139 {
140 inv[1]=1;
141 re(i,2,1000000)inv[i]=(mod-mod/i)*inv[mod%i]%mod;
142 }
143 //x=a[i](mod m[i])(1<=i<=n)
144 LL china(int n,int *a,int *m)//?D1¨²¨º¡ê¨®¨¤?¡§¨¤¨ª
145 {
146 LL M=1,d,y,x=0;
147 re(i,1,n)M*=m[i];
148 re(i,1,n)
149 {
150 LL w=M/m[i];
151 exgcd(m[i],w,d,d,y);
152 x=(x+y*w*a[i])%M;
153 }
154 return (x+M)%M;
155 }
156 //?a?¡ê¡¤?3¨¬a^x=b(mod n),n?a?¨º¨ºy
157 int log_mod(int a,int b,int n)//BSGS
158 {
159 int m,v,e=1;
160 m=(int)sqrt(n+1);
161 v=inv2(qpow(a,m,n),n);
162 map<int,int>x;
163 x[1]=0;
164 re(i,1,m-1)
165 {
166 e=e*a%n;
167 if(!x.count(e))x[e]=i;
168 }
169 re(i,0,m-1)
170 {
171 if(x.count(b))return i*m+x[b];
172 b=b*v%n;
173 }
174 return -1;
175 }
176 int prime_tot,mu[100010];
177 bool bo[100010];
178 void get_mu(int limit)//?a¡À¨¨?¨²?1o¡¥¨ºy
179 {
180 mu[1]=1;
181 re(i,2,limit)
182 {
183 if(!bo[i])prime[++prime_tot]=i,mu[i]=-1;
184 for(int j=1;j<=prime_tot&&i*prime[j]<=limit;j++)
185 {
186 bo[i*prime[j]]=1;
187 if(i%prime[j])mu[i*prime[j]]=-mu[i];
188 else {mu[i*prime[j]]=0;break;}
189 }
190 }
191 }
192 }
193 namespace Matrix
194 {
195 struct mat
196 {
197 int a[111][111],r,c;
198 void clear(int rr,int cc,int x)
199 {
200 r=rr,c=cc;
201 re(i,1,r)re(j,1,c)if(i==j)a[i][j]=x;
202 else a[i][j]=0;
203 }
204 int* op [] (int x){return x[a];}
205 mat op + (mat &rhs)
206 {
207 mat ret=*this;
208 re(i,1,r)re(j,1,c)ret[i][j]+=rhs[i][j];
209 return ret;
210 }
211 mat op - (mat &rhs)
212 {
213 mat ret=*this;
214 re(i,1,r)re(j,1,c)ret[i][j]-=rhs[i][j];
215 return ret;
216 }
217 mat op * (int &rhs)
218 {
219 mat ret=*this;
220 re(i,1,r)re(j,1,c)ret[i][j]*=rhs;
221 return ret;
222 }
223 mat op / (int &rhs)
224 {
225 mat ret=*this;
226 re(i,1,r)re(j,1,c)ret[i][j]/=rhs;
227 return ret;
228 }
229 mat op * (mat &rhs)
230 {
231 mat ret;ret.clear(r,rhs.c,0);
232 re(i,1,r)re(j,1,rhs.c)re(k,1,c)
233 ret[i][j]+=a[i][k]*rhs[k][j];
234 return ret;
235 }
236 mat qpow(int n)
237 {
238 mat ret,temp=*this;ret.clear(r,c,1);
239 while(n)
240 {
241 if(n&1)ret=ret*temp;
242 n>>=1;
243 temp=temp*temp;
244 }
245 return ret;
246 }
247 };
248 }
249 namespace gauss
250 {
251 const double eps=1e-8;
252 int n;
253 double a[111][111],x[111];
254 void xy1()
255 {
256 re(i,1,n)
257 {
258 if(abs(a[i][i])<eps)
259 re(j,i+1,n)if(abs(a[j][i])>eps)
260 {
261 re(k,i,n+1)swap(a[j][k],a[i][k]);
262 break;
263 }
264 re(j,i+1,n)
265 {
266 if(abs(a[j][i])<eps)continue;
267 double bi=a[i][i]/a[j][i];
268 re(k,i,n+1)a[j][k]*=bi;
269 re(k,i,n+1)a[j][k]-=a[i][k];
270 }
271 }
272 rre(i,n,1)
273 {
274 x[i]=a[i][n+1]/a[i][i];
275 rre(j,i-1,1)a[j][n+1]-=a[j][i]*x[i],a[j][i]=0;
276 }
277 }
278 LL fu[111],ans[111],aa[111][111],mod;
279 void xy2()
280 {
281 re(i,0,n-1)
282 re(j,i+1,n-1)
283 {
284 LL xia=aa[j][i],shang=aa[i][i];
285 re(k,i,n)
286 {
287 fu[k]=aa[i][k]*xia%mod;
288 aa[j][k]=aa[j][k]*shang%mod;
289 aa[j][k]=((aa[j][k]-fu[k])%mod+mod)%mod;
290 }
291 }
292 rre(i,n-1,0)
293 {
294 LL d,x,y;
295 using namespace nt;
296 exgcd(aa[i][i],mod,d,x,y);
297 aa[i][n]=aa[i][n]*x%mod,aa[i][i]=1;
298 rre(j,i-1,0)(aa[j][n]-=aa[j][i]*aa[i][n]%mod)%=mod,aa[j][i]=0;
299 }
300 }
301 }
302 int main()
303 {
304 return 0;
305 }
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