#include #include namespace nachia{ const unsigned int INPUT_BUF_SIZE = 2 << 20; const unsigned int OUTPUT_BUF_SIZE = 1 << 20; char input_buf[INPUT_BUF_SIZE]; struct input_buf_init{ input_buf_init(){ input_buf[fread(input_buf, 1, INPUT_BUF_SIZE-1, stdin)] = '\0'; } } input_buf_init_instance; struct input_buf_iterator{ private: unsigned int p = 0; public: static bool is_whitespace(char ch){ switch(ch){ case ' ': case '\n': case '\r': case '\t': return true; } return false; } void skip_whitespace(){ while(is_whitespace(input_buf[p])) p++; } unsigned int next_uint(){ skip_whitespace(); unsigned int buf = 0; while(true){ char tmp = input_buf[p]; if('9' < tmp || tmp < '0') break; buf = buf * 10 + (tmp - '0'); p++; } return buf; } int next_int(){ skip_whitespace(); if(input_buf[p] == '-'){ p++; return (int)(-next_uint()); } return (int)next_uint(); } unsigned long long next_ulong(){ skip_whitespace(); unsigned long long buf = 0; while(true){ char tmp = input_buf[p]; if('9' < tmp || tmp < '0') break; buf = buf * 10 + (tmp - '0'); p++; } return buf; } long long next_long(){ skip_whitespace(); if(input_buf[p] == '-'){ p++; return (long long)(-next_ulong()); } return (long long)next_ulong(); } char next_char(){ skip_whitespace(); return input_buf[p++]; } std::string next_token(){ skip_whitespace(); std::string buf; while(true){ char ch = input_buf[p]; if(is_whitespace(ch)) break; buf.push_back(ch); p++; } return buf; } }; char output_buf[OUTPUT_BUF_SIZE] = {}; struct fastoutput_table{ char dig3lz[1000][4]; char dig3nlz[1000][4]; fastoutput_table(){ for(unsigned int d=0; d<1000; d++){ unsigned int x = d; unsigned int i = 0; dig3lz[d][i++] = ('0' + x / 100 % 10); dig3lz[d][i++] = ('0' + x / 10 % 10); dig3lz[d][i++] = ('0' + x / 1 % 10); dig3lz[d][i++] = '\0'; } for(unsigned int d=0; d<1000; d++){ unsigned int x = d; unsigned int i = 0; if(x >= 100) dig3nlz[d][i++] = ('0' + x / 100 % 10); if(x >= 10) dig3nlz[d][i++] = ('0' + x / 10 % 10); if(x >= 1) dig3nlz[d][i++] = ('0' + x / 1 % 10); dig3nlz[d][i++] = '\0'; } } } fastoutput_table_inst; struct output_buf_iterator{ unsigned int p = 0; void next_char(char c){ output_buf[p++] = c; } void next_eoln(){ next_char('\n'); } void next_cstr(char* s){ int i = 0; while(s[i]) next_char(s[i++]); } void next_dig9(unsigned int x){ unsigned int y; y = x / 1'000'000; x -= y * 1'000'000; next_cstr(fastoutput_table_inst.dig3lz [y]); y = x / 1'000; x -= y * 1'000; next_cstr(fastoutput_table_inst.dig3lz [y]); y = x; next_cstr(fastoutput_table_inst.dig3lz [y]); } void next_uint(unsigned int x){ unsigned int y = 0; if(x >= 1'000'000'000){ y = x / 1'000'000'000; x -= y * 1'000'000'000; next_cstr(fastoutput_table_inst.dig3nlz[y]); next_dig9(x); } else if(x >= 1'000'000){ y = x / 1'000'000; x -= y * 1'000'000; next_cstr(fastoutput_table_inst.dig3nlz[y]); y = x / 1'000; x -= y * 1'000; next_cstr(fastoutput_table_inst.dig3lz [y]); next_cstr(fastoutput_table_inst.dig3lz [x]); } else if(x >= 1'000){ y = x / 1'000; x -= y * 1'000; next_cstr(fastoutput_table_inst.dig3nlz[y]); next_cstr(fastoutput_table_inst.dig3lz [x]); } else if(x >= 1){ next_cstr(fastoutput_table_inst.dig3nlz[x]); } else{ next_char('0'); } } void next_ulong(unsigned long long x){ unsigned int y = 0; if(x >= 1'000'000'000'000'000'000){ y = x / 1'000'000'000'000'000'000; x -= (unsigned long long)y * 1'000'000'000'000'000'000; next_uint(y); y = x / 1'000'000'000; x -= (unsigned long long)y * 1'000'000'000; next_dig9(y); next_dig9(x); } else if(x >= 1'000'000'000){ y = x / 1'000'000'000; x -= (unsigned long long)y * 1'000'000'000; next_uint(y); next_dig9(x); } else{ next_uint(x); } } void write_to_file(){ fwrite(output_buf, p, 1, stdout); } }; } // namespace nachia #include #include #include #include namespace nachia{ namespace prime_sieve_explicit_internal{ std::vector isprime = { false }; // a[x] := isprime(2x+1) void CalcIsPrime(int z){ if((int)isprime.size() *2+1 < z+1){ int new_z = isprime.size(); while(new_z*2+1 < z+1) new_z *= 2; z = new_z-1; isprime.resize(z+1, true); for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){ for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false; } } } std::vector prime_list = {2}; int prime_list_max = 0; void CalcPrimeList(int z){ while((int)prime_list.size() < z){ if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } void CalcPrimeListUntil(int z){ if(prime_list_max < z){ CalcIsPrime(z); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } } bool IsprimeExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n == 2) return true; if(n % 2 == 0) return false; CalcIsPrime(n); return isprime[(n-1)/2]; } int NthPrimeExplicit(int n){ using namespace prime_sieve_explicit_internal; CalcPrimeList(n); return prime_list[n]; } int PrimeCountingExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n < 2) return 0; CalcPrimeListUntil(n); auto res = ::std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin(); return (int)res; } // [l, r) ::std::vector SegmentedSieveExplicit(long long l, long long r){ assert(0 <= l); assert(l <= r); long long d = r - l; if(d == 0) return {}; ::std::vector res(d, true); for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){ long long il = (l+p-1)/p, ir = (r+p-1)/p; if(il <= p) il = p; for(long long i=il; i void DivisorZeta(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i*d] += a[i]; } template void DivisorInvZeta(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i] += a[i*d]; } template void DivisorMobius(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i*d] -= a[i]; } template void DivisorInvMobius(std::vector& a){ using namespace prime_sieve_explicit_internal; int n = a.size() - 1; for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i] -= a[i*d]; } template std::vector GcdConvolution(std::vector a, std::vector b){ assert(a.size() == b.size()); assert(1 <= a.size()); DivisorInvZeta(a); DivisorInvZeta(b); for(int i=1; i<(int)a.size(); i++) a[i] *= b[i]; DivisorInvMobius(a); return a; } template std::vector LcmConvolution(std::vector a, std::vector b){ assert(a.size() == b.size()); assert(1 <= a.size()); DivisorZeta(a); DivisorZeta(b); for(int i=1; i<(int)a.size(); i++) a[i] *= b[i]; DivisorMobius(a); return a; } } #include #include #include using namespace std; using i32 = int32_t; using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; #define rep(i,n) for(int i=0; i<(int)(n); i++) const i64 INF = 1001001001001001001; using modint = atcoder::static_modint<998244353>; int main(){ nachia::input_buf_iterator iitr; nachia::output_buf_iterator oitr; int N = iitr.next_uint(); int M = iitr.next_uint(); vector A(N+1, 0); rep(i,M){ A[iitr.next_uint()] = 1; } nachia::DivisorInvMobius(A); int ans = 0; rep(i,N) if(A[i+1] % 2 == 0) ans++; oitr.next_uint(ans); oitr.next_eoln(); oitr.write_to_file(); return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ std::ios::sync_with_stdio(false); std::cin.tie(nullptr); } } ios_do_not_sync_instance;