#include using namespace std; #include using namespace std; const long long MOD = 998244353; long long modpow(long long a, long long b){ long long ans = 1; while (b > 0){ if (b % 2 == 1){ ans *= a; ans %= MOD; } a *= a; a %= MOD; b /= 2; } return ans; } long long modinv(long long a){ return modpow(a, MOD - 2); } vector>> quotient_ranges(int N){ vector>> ans; for (int i = 1; i * i <= N; i++){ ans.push_back(make_pair(N / i, make_pair(i, i))); } for (int i = N / ((int) sqrt(N) + 1); i >= 1; i--){ ans.push_back(make_pair(i, make_pair(N / (i + 1) + 1, N / i))); } return ans; } long long sqrt_floor(long long N){ long long tv = 0, fv = 1100000000; while (fv - tv > 1){ long long mid = (tv + fv) / 2; if (mid * mid <= N){ tv = mid; } else { fv = mid; } } return tv; } bool is_square_number(long long N){ long long x = sqrt_floor(N); return x * x == N; } long long cbrt_floor(long long N){ long long tv = 0, fv = 1100000; while (fv - tv > 1){ long long mid = (tv + fv) / 2; if (mid * mid * mid <= N){ tv = mid; } else { fv = mid; } } return tv; } long long cbrt_ceil(long long N){ return cbrt_floor(N - 1) + 1; } pair, vector> dirichlet_sum_division(long long N, int K, int L, vector a, vector c, vector A, vector C){ vector b = c; long long INV_a1 = modinv(a[1]); for (int i = 1; i <= K; i++){ b[i] *= INV_a1; b[i] %= MOD; for (int j = i * 2; j <= K; j += i){ b[j] += MOD - a[j / i] * b[i] % MOD; b[j] %= MOD; } } vector asum(K + 1), bsum(K + 1); asum[0] = 0; bsum[0] = 0; for (int i = 1; i <= K; i++){ asum[i] = (asum[i - 1] + a[i]) % MOD; bsum[i] = (bsum[i - 1] + b[i]) % MOD; } vector B(L + 1, 0); for (int i = L; i >= 1; i--){ B[i] = C[i]; long long M = sqrt_floor(N / i); for (int j = 2; j <= M; j++){ if (N / i / j <= K){ B[i] += MOD - a[j] * bsum[N / i / j] % MOD; B[i] %= MOD; } else { B[i] += MOD - a[j] * B[i * j] % MOD; B[i] %= MOD; } } long long AM; if (M <= K){ AM = asum[M]; } else { AM = A[N / M]; } for (int j = 1; j <= M; j++){ if (N / i / j <= K){ B[i] += MOD - b[j] * asum[N / i / j] % MOD; } else { B[i] += MOD - b[j] * A[i * j] % MOD; } B[i] += b[j] * AM; B[i] %= MOD; } B[i] *= INV_a1; B[i] %= MOD; } return make_pair(b, B); } long long solve(long long N){ if (N == 0){ return 0; } vector small, large; int L = cbrt_ceil(N); int K = (N + L - 1) / L; vector a(K + 1, 0), c(K + 1, 0); vector A(L + 1, 0), C(L + 1, 0); for (int i = 1; i <= K; i++){ c[i] = 1; } for (int i : {1, 2, 3, 6}){ for (int j = 1; j * j * i <= K; j++){ a[j * j * i]++; } } for (int i = 1; i <= L; i++){ for (int j : {1, 2, 3, 6}){ A[i] += sqrt_floor(N / i / j); } C[i] = N / i; } vector b, B; tie(b, B) = dirichlet_sum_division(N, K, L, a, c, A, C); return B[1]; }; int main(){ long long L; int N; cin >> L >> N; vector A(N); for (int i = 0; i < N; i++){ cin >> A[i]; } vector P2 = {1}; while (P2.back() * 2 <= L){ long long x = P2.back() * 2; P2.push_back(x); } vector P3 = {1}; while (P3.back() * 3 <= L){ long long x = P3.back() * 3; P3.push_back(x); } int C2 = P2.size(); int C3 = P3.size(); vector> V(C2, vector(C3)); for (int i = 0; i < C2; i++){ for (int j = 0; j < C3; j++){ if (L / P2[i] < P3[j]){ V[i][j] = L + 1; } else { V[i][j] = P2[i] * P3[j]; } } } map> mp; for (int i = 0; i < C2; i++){ for (int j = 0; j < C3; j++){ if (V[i][j] <= L){ mp[V[i][j]] = make_pair(i, j); } } } vector> head(C2, vector(C3, false)); for (int i = 0; i < N; i++){ pair P = mp[A[i]]; head[P.first][P.second] = true; } for (int i = 0; i < C2; i++){ for (int j = 0; j < C3; j++){ if (head[i][j]){ for (int k = i; k < C2; k++){ for (int l = j; l < C3; l++){ if (!(k == i && l == j)){ head[k][l] = !head[k][l]; } } } } } } long long ans = 0; for (int i = 0; i < C2; i++){ for (int j = 0; j < C3; j++){ if (head[i][j] && V[i][j] <= L){ ans += solve(L / V[i][j]); } } } cout << ans << endl; }