3157: 国王奇遇记 & 3516: 国王奇遇记加强版 - BZOJ

果然我数学不行啊，题解君： http://www.cnblogs.com/zhuohan123/p/3726933.html

 

 1 const

 2     h=1000000007;

 3 var

 4     fac,facinv,powm,s:array[0..1100]of int64;

 5     n,m:int64;

 6 

 7 function mexp(a,b:int64):int64;

 8 begin

 9     if b=0 then exit(1);

10     mexp:=sqr(mexp(a,b>>1))mod h;

11     if b and 1=1 then mexp:=mexp*a mod h;

12 end;

13 

14 function C(n,r:int64):int64;

15 begin

16     exit((fac[n]*facinv[r] mod h)*facinv[n-r] mod h);

17 end;

18 

19 procedure main;

20 var

21     i,j:longint;

22 begin

23     read(n,m);

24     if m=1 then

25     begin

26       write((n*(n+1)div 2)mod h);

27       exit;

28     end;

29     fac[0]:=1;

30     for i:=1 to m do

31       fac[i]:=fac[i-1]*i mod h;

32     facinv[m]:=mexp(fac[m],h-2);

33     facinv[0]:=1;

34     for i:=m-1 downto 1 do

35       facinv[i]:=facinv[i+1]*(i+1)mod h;

36     powm[0]:=1;

37     for i:=1 to m do

38       powm[i]:=-powm[i-1];

39     s[0]:=((mexp(m,n+1)-m+h)mod h)*mexp(m-1,h-2)mod h;

40     for i:=1 to m do

41       begin

42         s[i]:=mexp(n,i)*mexp(m,n+1)mod h;

43         for j:=0 to i-1 do

44           s[i]:=(s[i]+powm[i-j]*(C(i,j)*s[j]mod h)+h)mod h;

45         s[i]:=s[i]*mexp(m-1,h-2)mod h;

46       end;

47     write(s[m]);

48 end;

49 

50 begin

51     main;

52 end.

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