結果

問題 No.2119 一般化百五減算
ユーザー noya2noya2
提出日時 2022-11-04 21:58:09
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 9,405 bytes
コンパイル時間 3,815 ms
コンパイル使用メモリ 266,628 KB
最終ジャッジ日時 2025-02-08 17:41:36
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 22 WA * 3
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ソースコード

diff # 

#line 1 "c.cpp"
#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for (int i = 0; i < int(n); ++i)
#define repp(i,n,m) for (int i = m; i < int(n); ++i)
#define reb(i,n) for (int i = int(n)-1; i >= 0; --i)
#define all(v) v.begin(),v.end()
using namespace std;
using namespace atcoder;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using PL = pair<long long, long long>;
using pdd = pair<long double, long double>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
template<class T>istream &operator>>(istream &is,vector<T> &v){for(auto &e:v)is>>e;return is;}
template<typename T>bool range(T a,T b,T x){return (a<=x&&x<b);}
template<typename T>bool rrange(T a,T b,T c,T d,T x,T y){return (range(a,c,x)&&range(b,d,y));}
template<typename T>void rev(vector<T> &v){reverse(v.begin(),v.end());}
void revs(string &s) {reverse(s.begin(),s.end());}
template<typename T>void sor(vector<T> &v, int f=0){sort(v.begin(),v.end());if(f!=0) rev(v);}
template<typename T>bool chmin(T &a,const T &b){if(a>b){a=b;return true;}return false;}
template<typename T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<typename T>void uniq(vector<T> &v){sor(v);v.erase(unique(v.begin(),v.end()),v.end());}
template<typename T1, typename T2>void print(pair<T1,T2> a);
template<typename T>void print(vector<T> v);
template<typename T>void print(vector<vector<T>> v);
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
void print(unsigned int a){ printf("%u", a); }
void print(unsigned long long a) { printf("%llu", a); }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template<typename T1,typename T2>void print(pair<T1,T2> a){print(a.first);print(),print(a.second);}
template<typename T>void print(vector<T> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())print();}}
template<typename T>void print(vector<vector<T>> v){for(auto ite=v.begin();ite!=v.end();){print(*ite);if(++ite!=v.end())out();}}
void yes(){out("Yes");}
void no (){out("No");}
void yn (bool t){if(t)yes();else no();}
void fast_io(){cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(20);}
void o(){out("!?");}

namespace noya2{

const int INF = 1001001007;
const long long mod1 = 998244353;
const long long mod2 = 1000000007;
const long long inf = 2e18;
const long double pi = 3.14159265358979323;
const long double eps = 1e-7;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

} // namespace noya2
using namespace noya2;

using mint = modint998244353;
void out(mint a){out(a.val());}
void out(vector<mint> a){vector<ll> b(a.size()); rep(i,a.size()) b[i] = a[i].val(); out(b);}
void out(vector<vector<mint>> a){for (auto v : a) out(v);}
istream &operator>>(istream &is,vector<mint> &v){for(auto &e:v){ll _x;is>>_x;e=_x;}return is;}

#line 2 "math.hpp"

#line 6 "math.hpp"

namespace noya2{

using namespace std;
using ll = long long;

ll safe_mod(ll a, ll m){ // m >= 1, 0 <= safe_mod(a,m) < m, safe_mod(a,m) = a (mod m)
    ll res = a % m;
    if (res < 0) res += m;
    return res;
} 

struct math{
    static ll gcd(ll a, ll b){return b?gcd(b,a%b):a;}
    static void ext_gcd1_plus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax + by = 1
        if (b == 0){ // a = 1
            x = 1, y = 0;
            return ;
        }
        ext_gcd1_plus(b, a%b, y, x);
        x = safe_mod(x,b);
        y = (1 - a * x) / b;
    }
    static void ext_gcd1_minus(ll a, ll b, ll &x, ll &y){ // gcd(a,b) = 1, a >= 0, b >= 0, ax - by = 1
        if (b == 0){ // a = 1
            x = 1, y = 0;
            return ;
        }
        ext_gcd1_plus(b, a%b, y, x);
        x = safe_mod(x,b);
        y = (a * x - 1) / b;
    }
};

ll safe_gcd(ll a, ll b){return math::gcd(abs(a),abs(b));} // safe_gcd(0,0) = 0, safe_gcd(c,0) = safe_gcd(0,c) = c
ll safe_lcm(ll a, ll b){return abs(a) / safe_gcd(a,b) * abs(b);}

struct line{
    ll a, b, c; // ax + by = c
    void norm(){ // a >= 0, if (a == 0) -> b >= 0, gcd(a,b,c) = 1
        if (a < 0) a = -a, b = -b, c = -c;
        if (a == 0) if (b < 0) b = -b, c = -c;
        ll g = safe_gcd(safe_gcd(a,b),c);
        a /= g, b /= g, c /= g;
    }
    line (ll _a = 1, ll _b = 0, ll _c = 0) : a(_a), b(_b), c(_c) {
        assert(_a != 0 || _b != 0);
        norm();
    }
    line (ll x1, ll y1, ll x2, ll y2){ // --- (x1,y1) --- (x2,y2) ---
        assert(x1 != x2 || y1 != y2);
        ll wx = x2 - x1, wy = y2 - y1;
        ll wg = safe_gcd(wx,wy);
        a = wy / wg, b = -wx / wg;
        c = a * x1 + b * y1;
        norm();
    }
    static line get_line(ll x1, ll y1, ll ex, ll ey){ // y = ey/ex (x - x1) + y1 
        return line(ey,-ex,ey*x1-ex*y1);
    }
    static line vertical_line(ll x1, ll y1, ll x2, ll y2){ // perpendicular bisector
        ll ex = y2 - y1, ey = x1 - x2;
        return line(ey*2,-ex*2,ey*(x1+x2)-ex*(y1+y2));
    }
    bool operator<(const line &rhs) const {
        return vector<ll>{a,b,c} < vector<ll>{rhs.a,rhs.b,rhs.c}; // to use set or map for line
    }
};

pair<ll,ll> ext_gcd(ll a, ll b, ll c){ // ax + by = c, |a|,|b|,|c| < 1e9, x <= max(|B|,|C|), y<= max(|A|,|C|)
    if (a < 0) return ext_gcd(-a,-b,-c);
    if (c < 0){
        pair<ll,ll> res = ext_gcd(a,b,-c);
        res.first = -res.first, res.second = -res.second;
        return res;
    }
    if (c == 0) return pair<ll,ll>(0,0);
    if (a == 0 && b == 0) return pair<ll,ll>(0,0); // answer not exist
    ll g = safe_gcd(a,b);
    if (c % g != 0) return pair<ll,ll>(0,0); // answer not exist
    a /= g, b /= g, c /= g;
    ll x, y;
    if (b == 0) return pair<ll,ll>(c,0);
    if (b > 0) math::ext_gcd1_plus(a,b,x,y);
    else math::ext_gcd1_minus(a,-b,x,y);
    x = safe_mod(x*c,abs(b));
    y = (c - a * x) / b;
    return pair<ll,ll>(x,y);
}

template<typename T>
T safe_ceil(T p, T q);

template<typename T>
T safe_floor(T p, T q){
    if (q < T(0)) return safe_floor(-p,-q);
    if (p >= T(0)) return p / q;
    return -safe_ceil(-p,q);
}

template<typename T>
T safe_ceil(T p, T q){
    if (q < T(0)) return safe_ceil(-p,-q);
    if (p >= T(0)) return (p + q - 1) / q;
    return -safe_floor(-p,q);
}

struct Eratosthenes{
    static vector<int> table;
    Eratosthenes (int Nmax = -1) {init(Nmax);}
    static void init(int Nmax){
        if (!table.empty()) return ;
        table.resize(Nmax+1,0);
        table[0] = 1, table[1] = 1;
        for (int p = 2; p <= Nmax; p++){
            if (table[p] != 0) continue;
            for (int j = p; j <= Nmax; j += p){
                table[j] = p;
            }
        }
    }
};
vector<int>Eratosthenes::table = vector<int>(0);

void build_eratosthenes(const int Nmax){Eratosthenes::init(Nmax);}

vector<pair<int,int>> fast_prime_factorization(int N){
    int pre = -1, cnt = 0;
    vector<pair<int,int>> res;
    while(true) {
        if (N == 1){
            if (cnt > 0) res.emplace_back(pre,cnt);
            break;
        }
        int div = Eratosthenes::table[N];
        if (pre != div){
            if (cnt > 0) res.emplace_back(pre,cnt);
            pre = div, cnt = 1;
        }
        else cnt++;
        N /= div;
    }
    return res;
}

bool fast_is_prime(int N){
    if (N <= 1) return false;
    return Eratosthenes::table[N] == N;
}

vector<pair<ll,int>> prime_factorization(ll N){
    vector<pair<ll,int>> res;
    ll iN = N;
    for (ll d = 2; d * d <= N; d++){
        if (iN % d != 0) continue;
        if (iN == 1) break;
        int ie = 0;
        while (iN % d == 0) iN /= d, ie++;
        res.emplace_back(d,ie);
    }
    if (iN != 1) res.emplace_back(iN,1);
    return res;
}

bool is_prime(ll N){
    if (N <= 1) return false;
    if (N <= 3) return true;
    for (ll d = 2; d * d <= N; d++){
        if (N % d == 0) return false;
    }
    return true;
}

}// namespace noya2
#line 78 "c.cpp"

void solve(){
    ll n, m; cin >> n >> m;
    ll l = 1;
    vector<ll> a(m), b(m);
    rep(i,m) cin >> a[i] >> b[i];
    rep(i,m){
        l = safe_lcm(l,a[i]);
        if (l > n){
            auto c = a, d = b;
            c.resize(i+1), d.resize(i+1);
            auto p = crt(b,a);
            if (p.second == 0 || p.first > n){
                out("NaN");
                return ;
            }
            ll x = p.first; bool ok = true;
            rep(j,m) if (safe_mod(x-b[j],a[j]) != 0) ok = false;
            if (ok) out(x);
            else out("NaN");
            return ;
        }
    }
    auto p = crt(b,a);
    if (p.second == 0 || p.first > n) out("NaN");
    else out(p.first);
}

int main(){
    fast_io();
    int t = 1; //cin >> t;
    while(t--) solve();
}
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