45 lines
811 B
C++
45 lines
811 B
C++
#include<cstdio>
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typedef long long LL;
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LL L; int kase;
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LL gcd(LL a,LL b) { return b?gcd(b,a%b):a; }
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inline LL mmul(LL a, LL b, LL m)
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{
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LL d=((long double)a/m*b+0.5);
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LL r=a*b-d*m;
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return r<0?r+m:r;
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}
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inline LL ksm(LL a,LL b,LL p)
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{
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LL res=1;
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for(;b;b>>=1,a=mmul(a,a,p)) b&1?res=mmul(res,a,p):0;
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return res;
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}
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inline LL phi(LL x)
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{
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LL res=x;
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for(LL i=2;i*i<=x;i++) if(x%i==0)
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{
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res=res/i*(i-1);
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while(x%i==0) x/=i;
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}
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if(x>1) res=res/x*(x-1);
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return res;
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}
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LL solve()
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{
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LL d=gcd(8,L);
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LL v=phi(9*L/d),i;
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for(i=1;i*i<=v;i++) if(v%i==0&&ksm(10,i,9*L/d)==1) return i;
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i--;
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for(;i>=1;i--) if(v%i==0&&ksm(10,v/i,9*L/d)==1) return v/i;
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return 0;
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}
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int main()
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{
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#ifdef local
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freopen("pro.in","r",stdin);
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#endif
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while(scanf("%lld",&L)==1&&L) printf("Case %d: %lld\n",++kase,solve());
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return 0;
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}
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