- #include <bits/stdc++.h>
- using namespace std;
- #define rep(i,a,n) for (long long i=a;i<n;i++)
- #define per(i,a,n) for (long long i=n-1;i>=a;i--)
- #define pb push_back
- #define mp make_pair
- #define all(x) (x).begin(),(x).end()
- #define fi first
- #define se second
- #define SZ(x) ((long long)(x).size())
- typedef vector<long long> VI;
- typedef long long ll;
- typedef pair<long long,long long> PII;
- const ll mod=1e9+7;
- ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
- // head
- long long _,n,c,k,a[11115],fib[11020]={0,1};
- namespace linear_seq
- {
- const long long N=10010;
- ll res[N],base[N],_c[N],_md[N];
- vector<long long> Md;
- void mul(ll *a,ll *b,long long k)
- {
- rep(i,0,k+k) _c[i]=0;
- rep(i,0,k) if (a[i]) rep(j,0,k)
- _c[i+j]=(_c[i+j]+a[i]*b[j])%mod;
- for (long long i=k+k-1;i>=k;i--) if (_c[i])
- rep(j,0,SZ(Md)) _c[i-k+Md[j]]=(_c[i-k+Md[j]]-_c[i]*_md[Md[j]])%mod;
- rep(i,0,k) a[i]=_c[i];
- }
- long long solve(ll n,VI a,VI b)
- { // a 系数 b 初值 b[n+1]=a[0]*b[n]+...
- // printf("%d\n",SZ(b));
- ll ans=0,pnt=0;
- long long k=SZ(a);
- assert(SZ(a)==SZ(b));
- rep(i,0,k) _md[k-1-i]=-a[i];_md[k]=1;
- Md.clear();
- rep(i,0,k) if (_md[i]!=0) Md.push_back(i);
- rep(i,0,k) res[i]=base[i]=0;
- res[0]=1;
- while ((1ll<<pnt)<=n) pnt++;
- for (long long p=pnt;p>=0;p--)
- {
- mul(res,res,k);
- if ((n>>p)&1)
- {
- for (long long i=k-1;i>=0;i--) res[i+1]=res[i];res[0]=0;
- rep(j,0,SZ(Md)) res[Md[j]]=(res[Md[j]]-res[k]*_md[Md[j]])%mod;
- }
- }
- rep(i,0,k) ans=(ans+res[i]*b[i])%mod;
- if (ans<0) ans+=mod;
- return ans;
- }
- VI BM(VI s)
- {
- VI C(1,1),B(1,1);
- long long L=0,m=1,b=1;
- rep(n,0,SZ(s))
- {
- ll d=0;
- rep(i,0,L+1) d=(d+(ll)C[i]*s[n-i])%mod;
- if (d==0) ++m;
- else if (2*L<=n)
- {
- VI T=C;
- ll c=mod-d*powmod(b,mod-2)%mod;
- while (SZ(C)<SZ(B)+m) C.pb(0);
- rep(i,0,SZ(B)) C[i+m]=(C[i+m]+c*B[i])%mod;
- L=n+1-L; B=T; b=d; m=1;
- }
- else
- {
- ll c=mod-d*powmod(b,mod-2)%mod;
- while (SZ(C)<SZ(B)+m) C.pb(0);
- rep(i,0,SZ(B)) C[i+m]=(C[i+m]+c*B[i])%mod;
- ++m;
- }
- }
- return C;
- }
- long long gao(VI a,ll n)
- {
- VI c=BM(a);
- c.erase(c.begin());
- rep(i,0,SZ(c)) c[i]=(mod-c[i])%mod;
- return solve(n,c,VI(a.begin(),a.begin()+SZ(c)));
- }
- };
- int main()
- {
- int T,ide=0;
- scanf("%d",&T);
- while(T--){
- scanf("%lld%lld%lld",&n,&c,&k);
- for(int i=2;i<10000;i++)fib[i]=(fib[i-1]+fib[i-2])%mod;
- for(int i=0;i<=101;i++)
- a[i]=powmod(fib[i*c],k);
- printf("Case %d:",++ide);
- VI qq;qq.clear();
- for(int i=0;i<=100;i++){
- if(i>0)(a[i]+=a[i-1])%=mod;
- qq.push_back(a[i]);
- }
- printf("%lld\n",linear_seq::gao(qq,n));
- }
- return 0;
- }
- #include<bits/stdc++.h>
- #define LL long long
- using namespace std;
- const LL MAXN = 111;
- long long aa,bb;
- LL K,C[MAXN], M[MAXN],x,y,m;
- LL gcd(LL a, LL b)
- {
- return b == 0 ? a : gcd(b, a % b);
- }
- LL exgcd(LL a, LL b, LL &x, LL &y)
- {
- if (b == 0)
- {
- x = 1, y = 0;
- return a;
- }
- LL r = exgcd(b, a % b, x, y), tmp;
- tmp = x;
- x = y;
- y = tmp - (a / b) * y;
- return r;
- }
- LL inv(LL a, LL b)
- {
- LL r = exgcd(a, b, x, y);
- while (x < 0)x+=b;
- return x;
- }
- int main()
- {
- int T;
- scanf("%d",&T);
- while(T--){
- K=3;
- for (LL i = 1; i <= K; i++)
- scanf("%lld", &M[i]);
- for (LL i = 1; i <= K; i++)
- scanf("%lld", &C[i]);
- bool flag = 1;
- for (LL i = 2; i <= K; i++)
- {
- LL M1 = M[i - 1], M2 = M[i], C2 = C[i], C1 = C[i - 1], T = gcd(M1, M2);
- if ((C2 - C1) % T != 0)
- {
- flag = 0;
- break;
- }
- M[i] = (M1 * M2) / T;
- C[i] = ( inv( M1 / T, M2 / T ) * (C2 - C1) / T ) % (M2 / T) * M1 + C1;
- C[i] = (C[i] % M[i] + M[i]) % M[i];
- }
- aa=C[K];
- for(int i=0;;i++){
- LL temp=1ll*i*i*i;
- temp%=M[K];
- if(temp==aa){
- printf("%d\n",i);
- break;
- }
- }
- }
- return 0;
- }
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