题目分析：

观察前3个点，$361=19*19$，所以可以发现实际上就是快速幂，然后模数猜测是$998244353$，因为功能编号里面有这个数字，用费马小定理处理一下。 $pts:12$

观察第4个点，读入很大而结果很小，说明模数不是很大，所以枚举法，配合欧拉定理可以求出来模数为$1145141$，很巧的是这个数是个质数，所以接下来同上。 $pts:7$

观察第5个点，读入很小而结果很大，那我们可以yy一下，读入里面有两个靠得很近的数，所以将读入排序之后求相邻的差值，会发现读入里面有：

$264708066$和$264708068$，输出是x=1996649514996338529和y=1589589654696467295，把$x*361-y$，这个数一定是模数的倍数。这个数等于$719200885258981741674$。

肉眼观察法发现这个数可以被$2$，被$3$整除，然后枚举发现可以被$23$整除，接着我们搞进linux的计算器里面发现剩下的$5211600617818708273$是个质数，所以模数就是它了。 $pts:9$

第6,7个点写了WA掉了，结合提示可以猜测是自然溢出了，而且是枚举乘法的时候溢出了，我们需要找出循环节。$pts:13$

观察第8,9,10个点，因为叫$2p$,所以猜测是prime的意思，也就是求$[l,r]$之间的prime，是质数为$"p"$，不是为$"."$。

最后一个点到了$10^18$的程度，但区间大小只有$10^6$。我想到了可以用区间的埃拉托斯特尼筛来做8,9号点，第十个点我就采用了压缩打表法。 $pts:18$

观察11,12,13个点，因为叫$2u$，所以猜测和$\mu$有关，也就是莫比乌斯函数，对于11,12号点，可以用8,9点的方法，对于13号点，我有一个绝妙的想法。

首先先判定质数，这一步可以用上面的表去判定。对于没判定到的数，用小于等于$10^6$的质数去筛它，这样是没筛干净的。

对于剩下的数，如果等于$1$，那么不用再判断了；如果大于$1e6$那么有三种情况，一种是它是个质数，一种是它是两个相同的质数的乘积，一种是它是两个不同的质数的乘积。所以对于第一种，miller-rabin，第二种，开方，第三种，除了上面两种。 $pts:20$

最后一个部分，14,15,16号点，因为叫$2g$，所以猜测和原根有关。14号点直接枚举，16号点可以先筛出质数，再判是否拟合，如果不拟合就直接break。

十五号点有点难。。我一开始想了一个线性筛的做法，是$O(8n)$的，但是超时了，看了KB的sol之后得到了启发。

对于一个原根g，只要g^d=x，且d与phi(p)互质，那么x就是一个原根

代码：

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                                                                                                                                                                                                                                                     oxXgXWxxpxptxxptWhxpxpxtNxnwWWxxpdGXwhwhpf^xTrxXhnOlkX`xtXxxdVxwtT@hxXprtxhxxpfWhxxutTvPPxxxwxvhutVxtvxxXoVxxxxNwxtx[uxxx@XwfpxvHpxxvLxwxpxxqpXHpvpXxXtxxXpxtppuXhn@ftvxODg_ajxxwhpnfxeXxWlktTxXx>hupWXhxxXpvxhvTxpxtWttxwWXvwttvvtpvfwxpANjxxHxxtxHppuxxwGxgxtPtnxsXxtnv`gxxvsvxwtgXwnFxxtvhwwXVxxdpvvwvxxxtxxwxxx`tTpVtvXxxPhfdxxXxhvn!xxThxrphpxxwWTvxxwrwXwxXPDtpXPxdNxhkxO@xlPhlnunxHfhpxxxlwvxpwxpxxx
                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                       xxrXhgxXxhHtgXpxHHv`nIxXxvXxvHZwvxhpwptpxTTpTXdvhwthOXvGhxvoxtw
                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                        
                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                                                           '9' || ch < '0') ch = getchar(); 25 int zz = 0; 26 while(ch<='9'&&ch>='0')zz=(zz*10ll+ch-'0')%(mod-1),ch=getchar(); 27 printf("%d\n",fast_pow(19,zz,mod)); 28 } 29 } 30 } 31 32 namespace solve2{ 33 int n; int mod=1145141; 34 void work(){ 35 scanf("%d",&n); 36 for(int i=1;i<=n;i++){ 37 char ch = getchar(); 38 while(ch > '9' || ch < '0') ch = getchar(); 39 int zz = 0; 40 while(ch<='9'&&ch>='0')zz=(zz*10ll+ch-'0')%(mod-1),ch=getchar(); 41 printf("%d\n",fast_pow(19,zz,mod)); 42 } 43 } 44 } 45 46 namespace solve3{ 47 int n; unsigned long long mod=5211600617818708273ll; 48 unsigned long long fast_multi(unsigned long long now,unsigned long long pw){ 49 unsigned long long dt = now,bit = 1,ans = 0; 50 while(bit <= pw){ 51 if(bit & pw){ans = ans+dt; if(ans >= mod) ans-=mod;} 52 dt = (dt+dt); if(dt >= mod) dt -= mod; 53 bit<<=1; 54 } 55 return ans; 56 } 57 unsigned long long fast_pow(int now,int pw){ 58 unsigned long long dt = now,bit = 1,ans = 1; 59 while(bit <= pw){ 60 if(bit & pw){ans = fast_multi(dt,ans);} 61 bit <<=1; dt = fast_multi(dt,dt); 62 } 63 return ans; 64 } 65 void work(){ 66 scanf("%d",&n); 67 for(int i=1;i<=n;i++){ 68 int zz; scanf("%d",&zz);printf("%llu\n",fast_pow(19,zz)); 69 } 70 } 71 } 72 73 namespace solve4{ 74 int n; const int mod = 998244353; 75 int res[102000]; 76 void work(){ 77 res[0] = 1; 78 for(int i=1;i<=100943;i++) res[i] = res[i-1]*19%mod; 79 scanf("%d",&n); 80 for(int i=1;i<=n;i++){ 81 long long zz; scanf("%lld",&zz); 82 if(zz > 100943) {zz -= 55245; zz %= 45699; zz += 55245;} 83 printf("%d\n",res[zz]); 84 } 85 } 86 } 87 88 namespace solve5{ 89 int n,prime[260000],flag[1000010],num; 90 void solveit(long long l,long long r){ 91 if(r <= 1e12+5){ 92 flag[1] = 1;int N = 1000000; 93 for(int i=2;i<=N;i++){ 94 if(!flag[i]) prime[++num] = i; 95 for(int j=1;j<=num&&i*prime[j]<=N;j++){ 96 flag[i*prime[j]] = 1; 97 if(i%prime[j] == 0) break; 98 } 99 }100 memset(flag,0,sizeof(flag));101 for(int i=1;i<=num;i++){102 long long st = l/prime[i]+(l%prime[i]!=0);103 if(st == 1) st++;104 for(long long j=st;j*prime[i]<=r;j++){105 flag[j*prime[i]-l+1] = 1;106 }107 }108 for(long long i=l;i<=r;i++)109 if(flag[i-l+1] == 1) printf(".");110 else printf("p");111 puts("");112 }else{113 for(int i=0;i
                                                                                                                                                                                                                                                          
                                                                                                                                                                                                                                                           '9') dd = ss[i]-'9';118 else{119 for(int j=i;j
                                                                                                                                                                                                                                                           
                                                                                                                                                                                                                                                            =0;j--) res[i*6+j] = (um&1),um>>=1;176 }177 for(int i=0;i
                                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                             '9') dd = ss[i]-'9';182 else{ for(int j=i;j
                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                               1e15){199 if(res[nur++] == 1) flag[i-l+1]*=-1;200 //printf("%lld %d\n",i,flag[i-l+1]);201 }else{flag[i-l+1] *= -1;}202 }203 if(flag[i-l+1] == 1) printf("+");204 else if(flag[i-l+1] == 0) printf("0");205 else printf("-");206 }207 puts("");208 }209 }210 void work(){211 scanf("%d",&n);212 for(int i=1;i<=n;i++){213 long long l,r; scanf("%lld%lld",&l,&r);214 if(i == 1){puts("--0-+-00+");}215 else if(i == 2){puts("-+-00+");}216 else if(i == 3){puts("--0-+-00+-0-++");}217 else solveit(l,r);218 }219 }220 }221 222 namespace solve8{223 void s99(int l,int r){224 int mod =998244353;225 for(int i=l;i<=r;i++){226 int flag = 0;227 if(fast_pow(i,(mod-1)/2,mod) == 1) flag = 1;228 if(fast_pow(i,(mod-1)/7,mod) == 1) flag = 1;229 if(fast_pow(i,(mod-1)/17,mod) == 1) flag = 1;230 if(flag) printf(".");231 else printf("g");232 }233 puts("");234 }235 int tab[23] = { 0,2,3,5,7,11,13,19,23};236 int gg = 6;237 int res[13500000];238 void s13(int l,int r,int p){239 for(int i=1;i<=p-1;i++,gg=1ll*gg*6%p){240 for(int j=1;j<=8;j++) if(i%tab[j] == 0) res[gg] = 1;241 }242 for(int i=1;i