bzoj3157 3516

太神了，被数学题虐了

orz http://m.blog.csdn.net/blog/skywalkert/43970331

这道题关键是抓住m较小的特点，构造递推解决

const mo=1000000007;

var c:array[0..1010,0..1010] of longint;
    f:array[0..1010] of int64;
    i,j,n,m:longint;
    t,ch:int64;

function quick(x:int64;y:longint):int64;
  begin
    quick:=1;
    while y>0 do
    begin
      if y mod 2=1 then quick:=quick*x mod mo;
      y:=y div 2;
      x:=x*x mod mo;
    end;
  end;

begin
  readln(n,m);
  c[0,0]:=1;
  for i:=1 to m do
  begin
    c[i,0]:=1;
    for j:=1 to i do
      c[i,j]:=(c[i-1,j]+c[i-1,j-1]) mod mo;
  end;
  if m=1 then
    writeln(int64(n)*int64(n+1) div 2 mod mo)
  else begin
    ch:=quick(m-1,mo-2);
    f[0]:=int64(m)*(quick(m,n)-1+mo) mod mo*ch mod mo;
    for i:=1 to m do
    begin
      f[i]:=quick(n,i)*quick(m,n+1) mod mo;
      for j:=0 to i-1 do
      begin
        t:=int64(c[i,j])*f[j] mod mo;
        if (i-j)  mod 2=1 then f[i]:=(f[i]-t+mo) mod mo
        else f[i]:=(f[i]+t) mod mo;
      end;
      f[i]:=f[i]*ch mod mo
    end;
    writeln(f[m]);
  end;
end.