1 namespace BigNumber{
2 const int L=5010,Base=10000,Bit=4;
3 const LL MaxInt=2147483647;
4 const int Pw10[15]={1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000};
5 const int Pw2[20]={1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536};
6
7 LL DOF[L];
8
9 struct BigNum{
10 int v[L],le,flag;
11 BigNum(){
12 memset(v,0,sizeof v); le=flag=1;
13 }
14 BigNum(int x){
15 flag=1; le=1; memset(v,0,sizeof v);
16 if (x<0) flag=-1,x=-x;
17 v[1]=x;
18 while (v[le]>=Base) v[le+1]+=v[le]/Base,v[le]%=Base,++le;
19 }
20 BigNum(LL x){
21 flag=1; le=1; memset(v,0,sizeof v);
22 if (x<0) flag=-1,x=-x;
23 v[1]=x%Base; v[2]=x/Base%Base;
24 v[3]=x/Base/Base%Base; v[4]=x/Base/Base/Base;
25 le=4;
26 while (v[le]>=Base) v[le+1]+=v[le]/Base,v[le]%=Base,++le;
27 while (v[le]==0 && le>1) --le;
28 }
29 BigNum(int len,int fir){
30 memset(v,0,sizeof v);
31 le=len; v[le]=fir; flag=1;
32 }
33 BigNum(const BigNum &a,int x){
34 memset(v,0,sizeof v);
35 le=a.le+x; flag=a.flag;
36 for (int i=1;i<=a.le;++i) v[i+x]=a.v[i];
37 }
38 int IntoInt(){
39 if (le>3) cerr <<"Error: cannot change so big into int!"<<endl;
40 LL d=0;
41 for (int i=le;i>=1;--i) d=d*Base+v[i];
42 if (flag==-1) d=-d;
43 if (d>MaxInt || -d<MaxInt+1) cerr <<"Error: cannot change so big into int!"<<endl;
44 return d;
45 }
46
47 void Clear(){
48 memset(v,0,sizeof v); le=flag=1;
49 }
50 void Tidy() {
51 if (le == 1 && !v[le]) flag = 1;
52 return;
53 }
54 void operator =(int a){
55 *this = BigNum(a);
56 }
57 void operator =(LL a){
58 *this = BigNum(a);
59 }
60
61
62 //Compare -->
63 bool operator ==(const BigNum &a)const{
64 if (le!=a.le || flag!=a.flag) return 0;
65 for (int i=1;i<=le;++i) if (v[i]!=a.v[i]) return 0;
66 return 1;
67 }
68 bool operator <(const BigNum &a)const{
69 if (flag < a.flag) return 1;
70 if (flag > a.flag) return 0;
71 if (le < a.le) return flag == 1 ? 1 : 0;
72 if (le > a.le) return flag == 1 ? 0 : 1;
73 for (int i=le;i>=1;--i){
74 if (v[i]<a.v[i]) return flag==1? 1:0;
75 if (v[i]>a.v[i]) return flag==1? 0:1;
76 }return 0;
77 }
78 bool operator >(const BigNum &a)const{
79 if (flag < a.flag) return 0;
80 if (flag > a.flag) return 1;
81 if (le < a.le) return flag == 1 ? 0 : 1;
82 if (le > a.le) return flag == 1 ? 1 : 0;
83 for (int i=le;i>=1;--i){
84 if (v[i]<a.v[i]) return flag==1? 0:1;
85 if (v[i]>a.v[i]) return flag==1? 1:0;
86 }return 0;
87 }
88 bool operator ==(const int &x)const{
89 return *this == BigNum(x);
90 }
91
92
93 //Add and Sub -->
94 void operator +=(const BigNum &x){
95 BigNum a=*this; BigNum b=x; memset(v,0,sizeof v);
96 flag=1;
97 if (a.flag==-1 && b.flag==-1){
98 flag=-1; a.flag=1; b.flag=1;
99 }
100 if (a < b) swap(a,b);
101 if (b.flag==-1){
102 b.flag=1;
103 if (a < b) swap(a,b),flag=-1;
104 b.flag=-1;
105 }
106 if (b.flag==1){
107 le=a.le;
108 for (int i=1;i<=le;++i) v[i]=a.v[i]+b.v[i];
109 for (int i=1;i<=le;++i) v[i+1]+=v[i]/Base,v[i]%=Base;
110 while (v[le+1]>0) ++le;
111 }else{
112 le=a.le;
113 for (int i=1;i<=le;++i) v[i]=a.v[i]-b.v[i];
114 for (int i=1;i<=le;++i) if (v[i]<0) --v[i+1],v[i]+=Base;
115 while (v[le]==0 && le>1) --le;
116 }
117 }
118 void operator +=(int x){
119 *this += BigNum(x);
120 }
121 void operator -=(const BigNum &x){
122 BigNum a=x; a.flag=-a.flag;
123 *this += a;
124 }
125 void operator -=(int x){
126 *this -= BigNum(x);
127 }
128
129
130 BigNum &operator ++(){
131 return *this += 1, *this;
132 }
133 BigNum &operator --(){
134 return *this -= 1, *this;
135 }
136 BigNum operator ++(int){
137 BigNum c(*this);
138 ++ *this; return c;
139 }
140 BigNum operator --(int){
141 BigNum c(*this);
142 -- *this; return c;
143 }
144
145
146 //Mul -->
147 void operator *=(const BigNum &x){
148 BigNum a=x;
149 if (flag==a.flag) flag=1;else flag=-1;
150 a.flag=1;
151
152 memset(DOF,0,sizeof DOF);
153 for (int i=1;i<=le;++i)
154 for (int j=1;j<=a.le;++j)
155 DOF[i+j-1]+=v[i]*a.v[j];
156 le+=a.le+9;
157 for (int i=1; i<=le; ++i) v[i]=0;
158 for (int i=1;i<=le;++i) DOF[i+1]+=DOF[i]/Base,DOF[i]%=Base;
159 while (DOF[le]==0 && le>1) --le;
160 for (int i=1;i<=le;++i) v[i]=DOF[i];
161 }
162 void operator *=(const int &x){
163 *this *= BigNum(x);
164 }
165 void operator *=(const LL &x){
166 *this *= BigNum(x);
167 }
168
169
170 //Div -->
171 void operator /=(int x){
172 if (x==0){
173 cerr <<"Error: div 0!"; return;
174 }
175 BigNum a; a=x;
176 if (flag==a.flag) flag=1;else flag=-1;
177 a.flag=1;
178 if (x < 0) x = -x;
179
180 memset(DOF,0,sizeof DOF);
181 LL rest=0;
182 for (int i=le;i>=1;--i){
183 rest=rest*Base+v[i];
184 DOF[i]=rest/x; rest%=x;
185 v[i]=0;
186 }
187 for (int i=le;i>=1;--i) v[i]=DOF[i];
188 while (v[le]==0 && le>1) --le;
189 }
190 void operator /=(const BigNum &x){
191 if (x==0){
192 cerr <<"Error: div 0!"; return;
193 }
194 BigNum a=*this,b=x,c,d;
195 if (a.flag==b.flag) flag=1;else flag=-1;
196 a.flag = b.flag = 1;
197 for (int i=le;i>0;--i) v[i]=0;
198 le=a.le-b.le+1;
199
200 for (int i=le;i>=1;--i){
201 c=BigNum(b,i-1);
202 for (int j=log2(Base);j>=0;--j){
203 d=c; d*=Pw2[j];
204 if (!(a < d)) v[i]+=Pw2[j],a-=d;
205 }
206 }
207 for (int i=1;i<=le;++i) v[i+1]+=v[i]/Base,v[i]%=Base;
208 while (v[le+1]>0) ++le;
209 while (v[le]==0 && le>1) --le;
210 }
211
212
213 //Mod -->
214 void operator %=(int p){
215 if (p==0){
216 cerr <<"Error: mod 0!"; return;
217 }
218 LL d=0; if (p < 0) p=-p;
219 for (int i=le;i>=1;--i) d=(d*Base+v[i])%p,v[i]=0;
220 le=1; v[1]=d;
221 while (v[le]>=Base) v[le+1]+=v[le]/Base,v[le]%=Base,++le;
222 }
223
224 void operator %=(const BigNum &x){
225 if (x==0){
226 cerr <<"Error: mod 0!"; return;
227 }
228 BigNum a=*this,b=x,c,d;
229 for (int i=le;i>0;--i) v[i]=0;
230 le=a.le-b.le+1;
231
232 for (int i=le;i>=1;--i){
233 c=BigNum(b,i-1);
234 for (int j=log2(Base);j>=0;--j){
235 d=c; d*=Pw2[j];
236 if (!(a < d)) a-=d;
237 }
238 }
239 *this = a;
240 }
241
242
243 //Power -->
244 BigNum pow(int b){
245 BigNum a,c; a=*this; c=1;
246 for (;b;b>>=1,a*=a) if (b&1) c*=a;
247 return c;
248 }
249 BigNum pow(int x,int b){
250 BigNum c,a; c=1; a=x;
251 for (;b;b>>=1,a*=a) if (b&1) c*=a;
252 return c;
253 }
254 int pow2(int a,int b){
255 int c=1;
256 for (;b;b>>=1,a*=a) if (b&1) c*=a;
257 return c;
258 }
259
260
261 //Shr and Shl -->
262 void operator <<=(int x){
263 if (x<=30) *this *= pow2(2,x);
264 else *this *= pow(2,x);
265 }
266 void operator >>=(int x){
267 if (x<=30) *this /= pow2(2,x);
268 else *this /= pow(2,x);
269 }
270
271
272 void rev() {
273 if (le > 1 || v[le]) flag = -flag;
274 return;
275 }
276
277 };
278
279
280 //Compare -->
281 bool operator ==(const int &a,const BigNum &b){
282 return b == a;
283 }
284 bool operator !=(const BigNum &a,const BigNum &b){
285 return !(a == b);
286 }
287 bool operator !=(const BigNum &a,const int &b){
288 return !(a == b);
289 }
290 bool operator !=(const int &a,const BigNum &b){
291 return !(b == a);
292 }
293
294
295 bool operator <(const BigNum &a,const int &b){
296 return a < BigNum(b);
297 }
298 bool operator <(const int &a,const BigNum &b){
299 return BigNum(a) < b;
300 }
301 bool operator >(const BigNum &a,const int &b){
302 return a > BigNum(b);
303 }
304 bool operator >(const int &a,const BigNum &b){
305 return BigNum(a) > b;
306 }
307 bool operator <=(const BigNum &a,const BigNum &b){
308 if (a > b) return 0; return 1;
309 }
310 bool operator >=(const BigNum &a,const BigNum &b){
311 if (a < b) return 0; return 1;
312 }
313 bool operator <=(const BigNum &a,const int &b){
314 if (a > b) return 0; return 1;
315 }
316 bool operator <=(const int &a,const BigNum &b){
317 if (a > b) return 0; return 1;
318 }
319 bool operator >=(const BigNum &a,const int &b){
320 if (a < b) return 0; return 1;
321 }
322 bool operator >=(const int &a,const BigNum &b){
323 if (a < b) return 0; return 1;
324 }
325
326
327 int max(const int &a,const int &b){
328 if (a < b) return b; return a;
329 }
330 int min(const int &a,const int &b){
331 if (a < b) return a; return b;
332 }
333 BigNum max(const BigNum &a,const BigNum &b){
334 if (a < b) return b; return a;
335 }
336 BigNum min(const BigNum &a,const BigNum &b){
337 if (a < b) return a; return b;
338 }
339
340
341 //Add -->
342 BigNum operator +(const BigNum &a,const BigNum &b){
343 BigNum c=a; c+=b; return c;
344 }
345 BigNum operator +(const BigNum &a,const int &b){
346 BigNum c=a; c+=b; return c;
347 }
348 BigNum operator +(const int &a,const BigNum &b){
349 BigNum c=b; c+=a; return c;
350 }
351
352
353 //Sub -->
354 BigNum operator -(const BigNum &a,const BigNum &b){
355 BigNum c=a; c-=b; return c;
356 }
357 BigNum operator -(const BigNum &a,const int &b){
358 BigNum c=a; c-=b; return c;
359 }
360 BigNum operator -(const int &a,const BigNum &b){
361 BigNum c=b; c-=a; return c;
362 }
363
364
365 //Mul -->
366 BigNum operator *(const BigNum &a,const BigNum &b){
367 BigNum c=a; c*=b; return c;
368 }
369 BigNum operator *(const BigNum &a,const int &b){
370 BigNum c=a; c*=b; return c;
371 }
372 BigNum operator *(const int &a,const BigNum &b){
373 BigNum c=b; c*=a; return c;
374 }
375
376
377 //Div -->
378 BigNum operator /(const BigNum &a,const int &b){
379 BigNum c=a; c/=b; return c;
380 }
381 BigNum operator /(const int &a,const BigNum &b){
382 BigNum c=b; c/=a; return c;
383 }
384 BigNum operator /(const BigNum &a,const BigNum &b){
385 BigNum c=a; c/=b; return c;
386 }
387
388
389 //Mod -->
390 BigNum operator %(const BigNum &a,const int &b){
391 BigNum c=a; c%=b; return c;
392 }
393 BigNum operator %(const int &a,const BigNum &b){
394 BigNum c=b; c%=a; return c;
395 }
396 BigNum operator %(const BigNum &a,const BigNum &b){
397 BigNum c=a; c%=b; return c;
398 }
399
400 //Shr and Shl -->
401 BigNum operator <<(const BigNum &a,const int b){
402 BigNum c=a; c<<=b; return c;
403 }
404 BigNum operator <<(const BigNum &a,BigNum &b){
405 return a << b.IntoInt();
406 }
407 BigNum operator >>(const BigNum &a,const int &b){
408 BigNum c=a; c>>=b; return c;
409 }
410 BigNum operator >>(const BigNum &a,BigNum &b){
411 return a >> b.IntoInt();
412 }
413
414
415 //Abs -->
416 BigNum abs(const BigNum &x){
417 BigNum c=x; c.flag=1; return c;
418 }
419
420
421 //Odd -->
422 int odd(const BigNum &x){
423 if (x.v[1] & 1) return 1; return 0;
424 }
425
426
427 //Gcd -->
428 BigNum gcd(const BigNum &x,const BigNum &y){
429 if (x.le == 1 && !x.v[1]) return y;
430 if (y.le == 1 && !y.v[1]) return x;
431 BigNum a=x,b=y,c=BigNum(1);
432 while (a!=b){
433 if (a < b) swap(a,b);
434 if (odd(a) && odd(b)) a-=b; else
435 if (odd(a)) b/=2; else
436 if (odd(b)) a/=2; else
437 a/=2,b/=2,c*=2;
438 }return a*c;
439 }
440
441
442 //Sqrt -->
443 BigNum sqrt(const BigNum &x){
444 if (x<0){
445 cerr <<"Error: sqrt nagetive!";
446 return 0;
447 }
448 BigNum l,r,m,A;
449 l=BigNum(x.le/2,1); r=BigNum(x.le/2+2,1);
450 while (l<=r){
451 m=(l+r)>>1;
452 if (m*m<=x) A=m,l=m+1; else r=m-1;
453 }return A;
454 }
455 BigNum sqrt(const BigNum &a,int b){
456 BigNum x=a;
457 if (x<0 && b%2==0){
458 cerr <<"Error: sqrt nagetive!";
459 return 0;
460 }
461 BigNum l,r,m,A;
462 int frog=x.flag; x.flag=1;
463 l=0; r=1;
464 while (r.pow(b)<x) l=r,r*=2;
465 while (l<=r){
466 m=(l+r)>>1;
467 if (m.pow(b)<=x) A=m,l=m+1; else r=m-1;
468 }
469 if (frog==-1) A.flag=-1;
470 return A;
471 }
472
473
474 //Read and Print -->
475 string yz; char cyz;
476 void Read(BigNum &a){
477 a.Clear();
478 while (cin.peek()==' ') getchar();
479 if (cin.peek()=='-'){
480 a.flag=-1; cin >>cyz;
481 }
482 cin >>yz;
483 int len=yz.length();
484 a.le=len/Bit;
485 for (int i=1;i<=a.le;++i){
486 int l=len-Bit*i,r=l+Bit-1;
487 for (int j=l;j<=r;++j) a.v[i]=a.v[i]*10+yz[j]-'0';
488 }
489 if(len%Bit!=0){
490 int r=len-Bit*a.le-1;
491 ++a.le;
492 for (int j=0;j<=r;++j) a.v[a.le]=a.v[a.le]*10+yz[j]-'0';
493 }
494 }
495
496 void PrintWith(int x,int k){
497 for (int i=k-1;i>=0;--i) if (Pw10[i]>x) putchar('0');
498 else putchar(x/Pw10[i]+'0'),x%=Pw10[i];
499 }
500 void Print(const BigNum &a){
501 if (a.flag==-1 && (a.le > 1 || a.v[a.le])) putchar('-');
502 printf("%d",a.v[a.le]);
503 for (int i=a.le-1;i>=1;--i) PrintWith(a.v[i],Bit);
504 }
505 void Println(const BigNum &a){
506 Print(a); puts("");
507 }
508 };
509
510 using namespace BigNumber;
