学步园

开始的时候被范围吓尿了，敲完之后嫌范围小。。。

#pragma comment(linker, "/STACK:102400000,102400000")
#include<iostream>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<queue>
#include<stack>
#include<string>
#include<map>
#include<set>
#include<cmath>
#include<cassert>
#include<cstring>
#include<iomanip>
using namespace std;
#ifdef _WIN32
#define i64 __int64
#define out64 "%I64d\n"
#define in64 "%I64d"
#else
#define i64 long long
#define out64 "%lld\n"
#define in64 "%lld"
#endif
/************ for topcoder by zz1215 *******************/
#define FOR(i,a,b)      for( int i = (a) ; i <= (b) ; i ++)
#define FF(i,a)        for( int i = 0 ; i < (a) ; i ++)
#define FFD(i,a,b)      for( int i = (a) ; i >= (b) ; i --)
#define S64(a)          scanf(in64,&a)
#define SS(a)           scanf("%d",&a)
#define LL(a)           ((a)<<1)
#define RR(a)           (((a)<<1)+1)
#define pb              push_back
#define pf              push_front
#define X               first
#define Y               second
#define CL(Q)           while(!Q.empty())Q.pop()
#define MM(name,what)   memset(name,what,sizeof(name))
#define MC(a,b)         memcpy(a,b,sizeof(b))
#define MAX(a,b)        ((a)>(b)?(a):(b))
#define MIN(a,b)        ((a)<(b)?(a):(b))
#define read            freopen("in.txt","r",stdin)
#define write           freopen("out.txt","w",stdout)

const int inf = 0x3f3f3f3f;
const i64 inf64 = 0x3f3f3f3f3f3f3f3fLL;
const double oo = 10e9;
const double eps = 10e-9;
const double pi = acos(-1.0);
const int maxc = 26;
const int maxz = 125;
const int mod = 12345;

int use;

struct Matrix
{
	int a[maxz][maxz];

	Matrix ()
	{
		MM(a,0);
	}

	void operator *= (const Matrix &y)
	{
		Matrix x;
		for(int i=0;i<use;i++)
		{
			for(int j=0;j<use;j++)
			{
				for(int k=0;k<use;k++)
				{
					x.a[i][j]+=a[i][k]*y.a[k][j];
					x.a[i][j]%=mod;
				}
			}
		}
		MC(a,x.a);
		return ;
	}

	Matrix pow(i64 n)
	{
		Matrix x,y;
		MC(y.a,a);
		for(int i=0;i<use;i++) x.a[i][i] = 1;
		while(n)
		{
			if(n%2==1)
			{
				x*=y;
			}
			y*=y;
			n/=2;
		}
		return x;
	}
};

i64 n;
int c;
vector<int>v[maxc+1];
int dp[maxz][maxz];
int f[maxc+1];
int s[maxc+1];
bool hash[maxc+1];
bool can[maxc+1][maxz];

bool yes(int x)
{
	for(int i=1;i<=maxc;i++)
	{
		if(hash[i])
		{
			int now = x%f[i];
			if(!can[i][now]) return false;
			x/=f[i];
		}
	}
	return true;
}

int start()
{
	Matrix ax,bx;
	MM(dp,0);

	int to,temp;
	for(int now=0;now<use;now++)
	{
		for(int i=1;i<=maxc;i++)
		{
			if(hash[i])
			{ 
				temp = now / s[i-1];
				temp %= f[i];
				to = now - temp*s[i-1];
				temp = (temp+1)%f[i];
				to += temp*s[i-1];
				dp[to][now]++;
			}
		}
	}

	MC(ax.a,dp);

	bx = ax.pow(n);

	int ans = 0;

	for(int i=0;i<use;i++)
	{
		if(yes(i))
		{
			ans+=bx.a[i][0];
			ans%=mod;
		}
	}
	return ans;
}

int main()
{
	while(cin>>n>>c)
	{
		char ch;
		int temp;
		MM(hash,false);
		MM(can,false);
		for(int i=0;i<=maxc;i++)
		{
			v[i].clear();
			f[i]=1;
		}
		for(int i=1;i<=c;i++)
		{
			cin>>ch>>temp;
			v[ch-'A'+1].pb(temp);
			f[ch-'A'+1]*=temp;
			int now = 0;
			while(now<maxz)
			{
				can[ch-'A'+1][now] = true;
				now+=temp;
			}
		}
		use=1;
		for(int i=1;i<=maxc;i++)
		{
			if(!v[i].empty())
			{
				use*=f[i];
				hash[i]=true;
			}
		}
		s[0]=f[0];
		for(int i=1;i<=maxc;i++)
		{
			s[i]=s[i-1]*f[i];
		}

		cout<<start()<<endl;

	}

	return 0;
}