Description

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alt=" " />
 

Input

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" alt=" " />

Output

aaarticlea/png;base64,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" alt=" " />
 

Sample Input

3 3

Sample Output

21
 

Data Constraint

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" 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" alt=" " />

考虑DP,我们设g[i]表示第i-m+1天~第i天为第一次出现非法方案的方案数,f[i]为第i天之前合法方案的方案数,h[i]为第i天前非法方案的方案数。

根据定义容易得出:h[i]=h[i-1]*m+g[i](即第i-1天前的方案数乘以第i天可召唤的种类加上g[i]

f[i]=mi-h[i]

g[i]=m!*f[i-m]-$\sum _{k=1}^{m-1}k!\ast g\left[ i-k\right]$=m!*mi-m-m!*h[i-m]-$\sum _{k=1}^{m-1}k!\ast g\left[ i-k\right]$

对于g[i],在m!*f[i-m]个方案中会存在一些不符合g[i]定义的方案,即不是第i-m+1天~第i天才开始出现第一次的非法方案。

如:对于序列.....5 4 1 2 3 4 5......(红色部分为g[i]的范围)

我们发现这个实际上在g[i-2]就出现非法方案了,不是g[i]的非法方案,我们需要减去这部分的方案。

我们发现,在上面这个序列,第i-2-5天到第i-2天是一个排列,第i-5天到第i天也是一个排列。

所以在第i-2-5天到第i-2天的某一个排列里,在第i-2天到第i天必有2!个方案多算的。

所以进一步整理我们可以得出g[i]=m!*f-[i-m]-1!*g[i-1]-2!*g[i-2]-…-(m-1)!*g[i-m+1],也就是上面那个例子。

所以我们得到了递推式:

g[i]=m!*mi-m-m!*h[i-m]-$\sum _limits{k=1}^{m-1}k!\ast g\left[ i-k\right]$

h[i]=h[i-1]*m+g[i]

不过这会超时,但是因为这是递推式,我们可以采用矩阵优化。

这是一个关于i的递推式,我们考虑列出矩阵出来。

mi-m
g[i-m+1]
g[i-m+2]
……
g[i-1]
hi-m

考虑它要转移到i+1的矩阵

mi-m+1
g[i-m+2]
g[i-m+3]
……
g[i]
hi-m+1

对照以上递推式我们得出转移的系数:

m           * mi-m
    1       g[i-m+1]
      ……     g[i-m+2]
        1   ……
m! -(m-1)! -(m-2)! …… -1! -m! g[i-1]
  1       m hi-m

(例:由mi-mmi-m+1是乘以一个m

因为hi-m+1=hi-m*m+g[i-m+1],所以g[i-m+1]的系数为1h[i-m]的系数为m,其余同理)

所以用个矩阵快速幂后就可以可以得出答案为mn-hn,即幂运算后的系数矩阵第一列的第一个数减去最后一次数即可。

 #include <cstring>
#include <cstdio>
#include <iostream>
#include <algorithm>
#define mo 1000000007
#define N 109
using namespace std;
long long ans,n,m;
struct data{
long long ju[N][N];
data operator * (const data &a) const{
data b;
for (long long i=;i<=m+;++i)
for (long long j=;j<=m+;++j){
b.ju[i][j]=;
for (long long k=;k<=m+;++k)
b.ju[i][j]=(b.ju[i][j]+ju[i][k]*a.ju[k][j]%mo+mo)%mo;
}
return b;
}
}qwq,tmp;
long long jie(long long x){
long long s=;
for (long long i=;i<=x;i++)
s=s*i%mo;
return s;
}
void kuai(){
long long b=n;
for (long long i=;i<=m+;++i) tmp.ju[i][i]=;
while (b){
if (b&) tmp=tmp*qwq;
qwq=qwq*qwq;
b>>=;
}
}
void init(){
scanf("%lld%lld",&n,&m);
qwq.ju[][]=m;
for (long long i=;i<=m-;++i)
qwq.ju[i][i+]=;
for (long long i=;i<=m;++i)
qwq.ju[m][i]=-jie(m-i+);
qwq.ju[m][]=jie(m);
qwq.ju[m][m+]=-qwq.ju[m][];
qwq.ju[m+][]=;
qwq.ju[m+][m+]=m;
}
void solve(){
ans=tmp.ju[][]-tmp.ju[m+][];
printf("%lld\n",(ans+mo)%mo);
}
int main(){
init();
kuai();
solve();
return ;
}

神奇的代码

(人生第一次写矩阵快速幂QAQ)

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