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| #include <bits/stdc++.h>
#define ll long long
const int cnt = 2500;
const int mod[] = {3, 5, 7, 11, 13, 17, 19, 23, 29};
ll fast_mul(ll a, ll b, ll m)
{
ll d = ((long double)a / m * b + 0.5);
ll r = a * b - d * m;
return r < 0 ? r + m : r;
}
ll fast_pow(ll a, ll m, ll n)
{
ll ret = 1;
while (m)
{
if (m & 1)
ret = fast_mul(ret, a, n);
a = fast_mul(a, a, n);
m >>= 1;
}
return ret;
}
bool check(ll k)
{
if (k <= 1)
return false;
if (k == 2)
return true;
if (!(k & 1))
return false;
ll t = k - 1;
int now = 0;
while (!(t & 1))
t >>= 1, ++now;
for (int i = 0; i < 9; i++)
{
if (mod[i] == k)
return 1;
ll x = fast_pow(mod[i], t, k), y = x;
for (int j = 1; j <= now; j++)
{
x = fast_mul(x, x, k);
if (x == 1 && !(y == 1 || y == k - 1))
return false;
y = x;
}
if (x != 1)
return 0;
}
return true;
}
int main()
{
srand(time(NULL));
ll k;
while (scanf("%llu", &k) == 1)
printf(check(k) ? "Y\n" : "N\n");
return 0;
}
|