160 lines
2.9 KiB
C++
160 lines
2.9 KiB
C++
#include<iostream>
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#include<algorithm>
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#include<cstdio>
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#include<queue>
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#include<map>
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#include<set>
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#include<cmath>
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#include<cstring>
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#include<iomanip>
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using namespace std;
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#define i64 __int64
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#define MM(name,what) memset(name,what,sizeof(name))
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const int inf = 0x3f3f3f3f;
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const i64 inf64 = 0x3f3f3f3f3f3f3f3fLL;
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const double oo = 10e9;
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const double eps = 10e-9;
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const double pi = acos(-1.0);
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const int maxn = 100111;
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const i64 mod = 364875103;
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const i64 mod1 = 97;
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const i64 mod2 = 3761599;
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const int maxc = 111;
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i64 gcd(i64 _a, i64 _b)
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{
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if (!_a || !_b)
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{
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return max(_a, _b);
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}
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i64 _t;
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while ((_t = _a % _b))
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{
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_a = _b;
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_b = _t;
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}
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return _b;
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}
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i64 ext_gcd (i64 _a, i64 _b, i64 &_x, i64 &_y)
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{
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if (!_b)
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{
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_x = 1;
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_y = 0;
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return _a;
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}
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i64 _d = ext_gcd (_b, _a % _b, _x, _y);
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i64 _t = _x;
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_x = _y;
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_y = _t - _a / _b * _y;
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return _d;
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}
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i64 invmod (i64 _a, i64 _p)
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{
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i64 _ans, _y;
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ext_gcd (_a, _p, _ans, _y);
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_ans < 0 ? _ans += _p : 0;
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return _ans;
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}
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i64 dp[maxn];
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i64 inv[maxn];
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i64 c[maxc][maxc];
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i64 n,m;
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i64 ans;
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i64 a[21];
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i64 cx;
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void init()
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{
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for(int i=1;i<maxn;i++)
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{
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inv[i]=invmod(i,mod2);
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}
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MM(c,0);
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for(int i=0;i<maxc;i++)
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{
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c[i][i]=1;
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c[i][0]=1;
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}
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for(int i=1;i<maxc;i++)
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{
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for(int j=1;j<maxc;j++)
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{
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c[i][j]=c[i-1][j-1]+c[i-1][j];
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c[i][j]%=mod1;
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}
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}
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cx = invmod(mod1,mod2);
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return ;
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}
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i64 lucas(i64 x,i64 y,i64 p=mod1)
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{
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if(y>x) return 0;
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i64 re=1;
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i64 dx = x%p;
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i64 dy = y%p;
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re*=c[dx][dy];
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dx = x/p;
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dy = y/p;
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if(dx || dy)
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{
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re*=lucas(dx,dy);
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}
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re%=p;
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return re;
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}
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i64 find(int x)
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{
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i64 t1 = lucas(n+x-1,x);
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i64 t2 = dp[x];
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i64 temp = cx;
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temp *= t2-t1;
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temp %= mod2;
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temp = (temp+mod2)%mod2;
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temp *= mod1;
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temp += t1;
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temp %= mod;
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return temp;
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}
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void start()
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{
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dp[0]=1;
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i64 now,temp;
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for(int i=1;i<=m;i++)
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{
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now = n+i-1;
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dp[i]=dp[i-1]*now;
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dp[i]%=mod2;
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dp[i]*=inv[i];
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dp[i]%=mod2;
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}
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return ;
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}
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int main()
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{
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init();
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int k,T;
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cin>>T;
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for(int tt=1;tt<=T;tt++)
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{
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cin>>n>>m;
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start();
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cin>>k;
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for(int i=1;i<=k;i++)
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{
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cin>>a[i];
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a[i]++;
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}
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ans=1;
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i64 pre = m;
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i64 now;
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for(int i=k;i>=1;i--)
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{
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now = pre - a[i]+1;
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ans *= find(now);
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ans %= mod;
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pre = a[i]-1;
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}
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cout<<"Case #"<<tt<<": "<<ans<<endl;
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}
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return 0;
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}
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