[斐波那契 数学技巧] 洛谷 P1306 斐波那契公约数

gcd(fib[n],fib[m])==fib[gcd(n,m)];

#include<cstdio>#include<cstdlib>#include<algorithm>using namespace std;typedef long long ll;namespace F{    struct Matrix{      ll a,b,c,d;      Matrix(ll a=0,ll b=0,ll c=0,ll d=0):a(a),b(b),c(c),d(d) { }    };    inline Matrix Mul(Matrix A,Matrix B,ll p){      return Matrix((A.a*B.a+A.b*B.c)%p,(A.a*B.b+A.b*B.d)%p,(A.c*B.a+A.d*B.c)%p,(A.c*B.b+A.d*B.d)%p);      }    inline Matrix Pow(Matrix a,ll b,ll p){      Matrix ret(1,0,0,1);      for (;b;b>>=1,a=Mul(a,a,p))        if (b&1)      ret=Mul(ret,a,p);      return ret;    }    inline ll f(ll n,ll p){      if (!n) return 0;      return Pow(Matrix(1,1,1,0),n-1,p).a;    }  }int main(){  int n,m;  freopen("t.in","r",stdin);  freopen("t.out","w",stdout);  scanf("%d%d",&n,&m);  n=__gcd(n,m);  printf("%lld\n",F::f((ll)n,100000000LL));  return 0;}