"Fermat theorem + fast Power + inverse" bzoj3240-[noi2013] matrix game

"The main topic"

If you use F[i][j] to represent the elements of column I, J, in the Matrix, then F[i][j] satisfies the following recursion:
F[1][1]=1
F[i,j]=a*f[i][j-1]+b (j!=1) ①
F[i,1]=c*f[i-1][m]+d (i!=1) ②
The a,b,c,d in a recursive style is a given constant. F[N][M].

Ideas

Grind for a morning, however the extra data on the UOJ is not over yet. Bzoj on the AC first put up, follow slowly grind ...

* There is a point, the final output of the answer when the first +mod and then%mod.

*mod be diligent, or it will explode.

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5 #defineMOD 10000000076 using namespacestd;7typedefLong Longll;8 Const intmaxn=1000000+5;9 structnodeTen { Onell Uni,ord;//Uni means A≠1,ord represents a=1 A }n,m; - ll A,b,c,d; -  the ll Quick (ll X,ll p) - { -ll res=p,retu=1, now=x; -      while(res>0) +     { -         if(res&1) retu= (retu*now)%MOD; +now= (now*now)%MOD; Ares>>=1; at     } -     returnRetu; - } -  - ll Ni (ll x) - { in     returnQuick (x,mod-2); - } to  +Node Get_value (Charstr[]) - { the     intlen=strlen (str); *Node ret= (node) {0,0};  $      for(intI=0; i<len;i++)Panax Notoginseng     { -Ret.uni= ((ret.uni*Ten)% (mod-1) +str[i]-'0')% (mod-1); theRet.ord= ((ret.ord*Ten)%mod+str[i]-'0')%MOD; +     } A     returnret; the }  +  - voidInit () $ { $     CharSTRM[MAXN],STRN[MAXN]; -scanf"%s%s", STRN,STRM); -n=get_value (STRN); them=get_value (STRM); -scanf"%lld%lld%lld%lld",&a,&b,&c,&d);Wuyi } the  - voidGet_ans () Wu { -ll F;//=f[n+1][1] About     if(a==1) $     { -ll D= ((((C* (m.ord-1))%mod) *b)%mod+d)%MOD; -         if(c==1) f= (1+N.ORD*D)%MOD; -             Else A             { +ll cn=Quick (C,n.uni); theF= (cn+ (d* (cn-1) *ni (C-1) (%mod))%MOD; -             }  $     } the     if(a!=1) the     { thell Am=quick (a,m.uni-1); thell a= (am*c)%MOD; -ll b= (((((b*c)%mod* (am-1))%mod*ni (A-1))) (%mod+d)%MOD; inll an=Quick (A,n.uni); theF=an+ ((b* (an-1)%mod) *ni (A-1))%MOD; the     } Aboutprintf"%lld", ((f-d) *ni (c)%mod+mod)%MOD);  the } the  the intMain () + { - init (); the Get_ans ();Bayi     return 0; the}

"Fermat theorem + fast Power + inverse" bzoj3240-[noi2013] matrix game