HDU 1796How Many integers can you find (Repulsion principle)

How many integers can you findTime limit:5000MS Memory Limit:32768KB 64bit IO Format:%i64d &%i64 U SubmitStatusPracticeHDU 1796

Description

Now you get a number N, and a m-integers set, you should find out how many integers which is small than N, that they can Divided exactly by any integers in the set. For example, n=12, and M-integer set are {2,3}, so there are another set {2,3,4,6,8,9,10}, all the integers of the set can B e divided exactly by 2 or 3. As a result, you just output the number 7.

Input

There is a lot of cases. For each case, the first line contains integers N and M. The follow line contains the M integers, and all of the them is different from each other. 0<n<2^31,0<m<=10, and the M integer is non-negative and won ' t exceed 20.

Output

For each case, output the number.

Sample Input

12 2 2 3

Sample Output

7 Analysis: These days to learn to have feelings, know is tolerant, but there is a problem, coprime is the number, and then for 2,4 such a number will not do, too superficial, directly seek least common multiple ah, yes, coprime multiplication is because least common multiple is the product AH =_=, weak!

1#include <iostream>2#include <cstring>3#include <cstdio>4#include <algorithm>5 using namespacestd;6typedefLong LongLL;7 intnum[ -], N, M, a[ -];8 LL Res;9 ll GCD (ll A, ll b)Ten { One     if(A = =0) A         returnb; -     returnGCD (b%A, a); - } the voidDfsintCurintSnum,intCNT) - { -     if(Snum = =CNT) -     { +         inttemp =N; -         intMult =1; +          for(inti =0; i < Snum; i++) Amult = MULT/GCD (mult, a[i]) * A[i];//Explosion Proof at         if(Mult = =0) -             return; -         if(temp% Mult = =0) -Res + = Temp/mult-1; -         Else -Res + = temp/mult; in         return; -     } to      for(inti = cur; I < m; i++) +     { -A[snum] =Num[i]; theDFS (i +1, Snum +1, CNT); *     } $ }Panax Notoginseng intMain () - { the     intTM; +      while(SCANF ("%d%d", &n, &AMP;TM)! =EOF) A     { them =0; +          for(inti =0; I < TM; i++) -         { $             inttemp; $scanf"%d", &temp);//go to 0 -             if(temp) -num[m++] =temp; the         } -LL sum =0;Wuyi          for(inti =1; I <= m; i++) the         { -res =0; WuDfs0,0, i); -             if(I &1) AboutSum + =Res; $             Else -Sum-=Res; -         } -printf"%i64d\n", sum); A     } +     return 0; the}

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HDU 1796How Many integers can you find (Repulsion principle)