#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 998244353; // constexpr int MOD = 1000000007; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; long long mod_inv(long long a, const int m) { if ((a %= m) < 0) a += m; if (std::__gcd(a, static_cast(m)) != 1) return -1; long long x = 1; for (long long b = m, u = 0; b > 0;) { const long long q = a / b; std::swap(a -= q * b, b); std::swap(x -= q * u, u); } x %= m; return x < 0 ? x + m : x; } template std::pair chinese_remainder_theorem(std::vector b, std::vector m) { const int n = b.size(); T x = 0, md = 1; for (int i = 0; i < n && md < numeric_limits::max(); ++i) { if ((b[i] %= m[i]) < 0) b[i] += m[i]; if (md < m[i]) { std::swap(x, b[i]); std::swap(md, m[i]); } if (md % m[i] == 0) { if (x % m[i] != b[i]) return {0, 0}; continue; } const T g = std::__gcd(md, m[i]); if ((b[i] - x) % g != 0) return {0, 0}; const T u_i = m[i] / g; x += (b[i] - x) / g % u_i * mod_inv(md / g, u_i) % u_i * md; md *= u_i; if (x < 0) x += md; } return {x, md}; } int main() { int n, m; cin >> n >> m; vector b(m), c(m); REP(i, m) { cin >> b[i] >> c[i]; c[i] %= b[i]; if (c[i] < 0) c[i] += b[i]; } const auto [ans, md] = chinese_remainder_theorem(c, b); if (md == 0 || ans > n) { cout << "NaN\n"; return 0; } REP(i, m) { if (ans % b[i] != c[i]) { cout << "NaN\n"; return 0; } } cout << ans << '\n'; return 0; }