方法：数论
其实不是很明白，为什么这个公式可行
a^b % m = a^(b%phi[m] + phi[m]) % m
code:
1 #include <cstdio> 2 #include <cstring> 3 #include <algorithm> 4 #include <iostream> 5 #include <string> 6 #include <vector> 7 #include <stack> 8 #include <bitset> 9 #include <cstdlib> 10 #include <cmath> 11 #include <set> 12 #include <list> 13 #include <deque> 14 #include <map> 15 #include <queue> 16 #include <fstream> 17 #include <cassert> 18 #include <unordered_map> 19 #include <unordered_set> 20 #include <cmath> 21 #include <sstream> 22 #include <time.h> 23 #include <complex> 24 #include <iomanip> 25 #define Max(a,b) ((a)>(b)?(a):(b)) 26 #define Min(a,b) ((a)<(b)?(a):(b)) 27 #define FOR(a,b,c) for (ll (a)=(b);(a)<(c);++(a)) 28 #define FORN(a,b,c) for (ll (a)=(b);(a)<=(c);++(a)) 29 #define DFOR(a,b,c) for (ll (a)=(b);(a)>=(c);--(a)) 30 #define FORSQ(a,b,c) for (ll (a)=(b);(a)*(a)<=(c);++(a)) 31 #define FORC(a,b,c) for (char (a)=(b);(a)<=(c);++(a)) 32 #define FOREACH(a,b) for (auto &(a) : (b)) 33 #define rep(i,n) FOR(i,0,n) 34 #define repn(i,n) FORN(i,1,n) 35 #define drep(i,n) DFOR(i,n-1,0) 36 #define drepn(i,n) DFOR(i,n,1) 37 #define MAX(a,b) a = Max(a,b) 38 #define MIN(a,b) a = Min(a,b) 39 #define SQR(x) ((LL)(x) * (x)) 40 #define Reset(a,b) memset(a,b,sizeof(a)) 41 #define fi first 42 #define se second 43 #define mp make_pair 44 #define pb push_back 45 #define all(v) v.begin(),v.end() 46 #define ALLA(arr,sz) arr,arr+sz 47 #define SIZE(v) (int)v.size() 48 #define SORT(v) sort(all(v)) 49 #define REVERSE(v) reverse(ALL(v)) 50 #define SORTA(arr,sz) sort(ALLA(arr,sz)) 51 #define REVERSEA(arr,sz) reverse(ALLA(arr,sz)) 52 #define PERMUTE next_permutation 53 #define TC(t) while(t--) 54 #define forever for(;;) 55 #define PINF 1000000000000 56 #define newline ' ' 57 58 #define test if(1)if(0)cerr 59 using namespace std; 60 using namespace std; 61 typedef vector<int> vi; 62 typedef vector<vi> vvi; 63 typedef pair<int,int> ii; 64 typedef pair<double,double> dd; 65 typedef pair<char,char> cc; 66 typedef vector<ii> vii; 67 typedef long long ll; 68 typedef unsigned long long ull; 69 typedef pair<ll, ll> l4; 70 const double pi = acos(-1.0); 71 72 int phi(int n) 73 { 74 int ret = n; 75 for (int i = 2; i * i <= n; ++i) 76 { 77 if (n % i) continue; 78 ret -= ret/i; 79 while (n % i == 0) n /= i; 80 } 81 if (n != 1) 82 ret -= ret/n; 83 return ret; 84 } 85 int m, n; 86 int a[10]; 87 ll pow_mod(ll base, ll p, ll mod) 88 { 89 if (!base) return 0; 90 ll ret = 1; 91 while (p) 92 { 93 if (p & 1) ret = ret * base % mod; 94 p >>= 1; 95 base = base * base % mod; 96 } 97 return ret; 98 } 99 int dfs(int cur, int mod) 100 { 101 if (cur == n-1) return a[cur] % mod; 102 int ph = phi(mod); 103 return pow_mod(a[cur], dfs(cur+1, ph)%ph + ph, mod); 104 } 105 int main() 106 { 107 int kase = 0; 108 while (cin >> m >> n) 109 { 110 rep(i, n) cin >> a[i]; 111 cout << "Case #" << ++kase << ": " << dfs(0, m) << newline; 112 } 113 } 114 /* 115 10 4 2 3 4 5 116 100 2 5 2 117 53 3 2 3 2 118 # 119 */