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Cod sursa(job #543620)
/* O(2^K * K) */
#include <cstdio>
#include <vector>
#define ll long long
using namespace std;
ll N, sol;
int K, d[32], st[32], comb[32][32], proc[32];
inline int bit(int x, int nr)
{ return (x & (1<<nr)) != 0; }
inline ll gcd(ll a, ll b)
{ return b ? gcd(b, a%b) : a; }
int main()
{
freopen ( "light2.in", "r", stdin ) ;
freopen ( "light2.out", "w", stdout ) ;
scanf("%lld%d", &N, &K);
for (int i = 0; i < K; ++i)
scanf("%d", &d[i]);
comb[1][0] = comb[1][1] = 1;
for (int i = 2; i <= K; ++i)
{
comb[i][0] = 1;
for (int j = 1; j <= i; ++j)
comb[i][j] = comb[i-1][j-1] + comb[i-1][j];
}
for (int i = 1; i <= K; ++i)
for (int j = 1; j <= i; j += 2)
proc[i] += comb[i][j];
int nrb;
ll multiple;
for (int i = 1; i < (1<<K); ++i)
{
nrb = 0; multiple = 1;
for (int j = 0; j < K; ++j)
if (bit(i, j))
{
++nrb;
multiple = multiple * d[j] / gcd(multiple, d[j]);
if (multiple > N)
break;
}
if (multiple <= N)
{
if (nrb & 1)
sol += (N / multiple) * proc[nrb];
else
sol -= (N / multiple) * proc[nrb];
}
}
printf("%lld\n", sol);
return 0;
}