Problem X
Huge Mod
Input: standard input
Output: standard output
Time Limit: 1 second
The
operator for exponentiation is different from the addition, subtraction,
multiplication or division operators in the sense that the default associativity
for exponentiation goes right to left instead of left to right. So unless we
mess it up by placing parenthesis, 
should mean
not 
. This leads to the
obvious fact that if we take the levels of exponents higher (i.e., 2^3^4^5^3),
the numbers can become quite big. But let‘s not make life miserable. We being
the good guys would force the ultimate value to be no more than 10000.
Given a1, a2, a3, ... ,
aN and m(=10000)
you only need to compute
a1^a2^a3^...^aN mod m.
Input
Therecan be multiple (not more than 100) test cases. Each test case will be presented
in a single line. The first line of each test case would contain the value for
M(2<=M<=10000). The next number of that line would be N(1<=N<=10).
Then N numbers - the values for a1,
a2,
a3,
... , aN would
follow. You can safely assume that 1<=ai<=1000.
The end of input is marked by a line containing a single hash (‘#‘) mark.
Output
Foreach of the test cases, print the test case number followed by the value of
a1^a2^a3^...^aN mod
m on one line. The sample output shows the exact format for printing the test
case number.
Sample Input | Sample Output |
10 4 2 3 4 5 100 2 5 2 53 3 2 3 2 # | Case #1: 2 Case #2: 25 Case #3: 35 |
题意：求出 a0^a1^a2......a^n%m的值。
sl: 以前做过一个a^B mod 1e9+7 的题，那个很显然是费马小定理。碰见这个题目傻逼了。
百度学习一翻知：A^x=A^(x%phi[[m]+phi[m]) (phi[m]<=x) 很显然一个递归的式子。
哎，但是当时每次都是对x%phi[MOD] 傻叉了。应该递归求解。
坑了我4个点真吭。。。