Power Tower（广义欧拉降幂）

题意：https://codeforc.es/contest/906/problem/D

计算区间的：

ai ^ ai+1 ^ ai+2.......ar 。

思路：

广义欧拉降幂：

注意是自下而上递归使用欧拉降幂，比如求：a^b^c == a^(b^c%phi(mod)+?) == a^(b^(c%phi(phi(mod))+?+?)

而不是：a^b^c == a^b^(c%phi(mod)+?) == a^(b^(c%phi(mod)+?)%phi(mod)+?)  这样本身就是不对的，次方不是这么算的。

注意：因为判断要不要+phi（mod），所有快速幂里面就要开始搞搞，自己标个flag，或者直接重定义Mod == return x>=m?x%m+m:x;

注意：快速幂里的break

 #define IOS ios_base::sync_with_stdio(0); cin.tie(0);
 #include <cstdio>//sprintf islower isupper
 #include <cstdlib>//malloc  exit strcat itoa system("cls")
 #include <iostream>//pair
 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\草稿.txt","r",stdin);
 #include <bitset>
 #include <map>
 //#include<unordered_map>
 #include <vector>
 #include <stack>
 #include <set>
 #include <string.h>//strstr substr
 #include <string>
 #include <time.h>//srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
 #include <cmath>
 #include <deque>
 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
 #include <vector>//emplace_back
 //#include <math.h>
 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
 #define fo(a,b,c) for(register int a=b;a<=c;++a)
 #define fr(a,b,c) for(register int a=b;a>=c;--a)
 #define mem(a,b) memset(a,b,sizeof(a))
 #define pr printf
 #define sc scanf
 #define ls rt<<1
 #define rs rt<<1|1
 typedef long long ll;
 void swapp(int &a,int &b);
 double fabss(double a);
 int maxx(int a,int b);
 int minn(int a,int b);
 int Del_bit_1(int n);
 int lowbit(int n);
 int abss(int a);
 //const long long INF=(1LL<<60);
 const double E=2.718281828;
 const double PI=acos(-1.0);
 const int inf=(<<);
 const double ESP=1e-;
 //const int mod=(int)1e9+7;
 const int N=(int)1e6+;

 ll a[N];
 map<ll,ll>mp;
 long long phi(long long n)//a^(b mod phi(c)+phi(c)) mod c
 {
     if(mp.count(n))return mp[n];//记忆化;
     long long i,rea=n,temp=n;
     for(i=;i*i<=n;i++)
     {
         if(n%i==)
         {
             rea=rea-rea/i;
             while(n%i==)
                 n/=i;
         }
     }
     if(n>)
         rea=rea-rea/n;
     mp[temp]=rea;
     return rea;
 }
 ll Mod(ll x, ll m)
 {
     return x>=m?x%m+m:x;
 }
 long long qpow(long long a,long long b,long long mod)
 {
     long long ans,fl=;
 //    ll ta=a,tb=b,tta=a;
     ans=;
     while(b!=)
     {
         if(b&)
         {
             if(ans*a>=mod)fl=;
             ans=ans*a%mod;
         }
         b/=;
         if(!b)break;
         if(a*a>=mod)fl=;
         a=a*a%mod;
     }
     return ans+(fl?mod:);
 }
 ll solve(int l,int r,ll mod)//返回l~r计算结果;    听说phi(phi(mod))~==~mod/2所有最多log次;
 {
     if(l==r||mod==)return Mod(a[l],mod);//任何数%1都是0,不用再算了;
     return qpow(a[l],solve(l+,r,phi(mod)),mod);//假设我已经知道了l+1~r的结果:递归下去;
 }

 int main()
 {
     int n;
     ll p;
     sc("%d%lld",&n,&p);
     fo(i,,n)sc("%lld",&a[i]);
     int ask;sc("%d",&ask);
     while(ask--)
     {
         int l,r;
         sc("%d%d",&l,&r);
         pr("%lld\n",solve(l,r,p)%p);
     }
     return ;
 }

 /**************************************************************************************/

 int maxx(int a,int b)
 {
     return a>b?a:b;
 }

 void swapp(int &a,int &b)
 {
     a^=b^=a^=b;
 }

 int lowbit(int n)
 {
     return n&(-n);
 }

 int Del_bit_1(int n)
 {
     return n&(n-);
 }

 int abss(int a)
 {
     return a>?a:-a;
 }

 double fabss(double a)
 {
     return a>?a:-a;
 }

 int minn(int a,int b)
 {
     return a<b?a:b;
 }