#include #include #include #include #include #include #include #include using namespace std; typedef long long ll; #define rep(i, n) for(int i = 0; i < (n); i++) template using vi = vector; template using vii = vector>; template using viii = vector>; void chmax(ll & x, ll y) { x = max(x, y); } ll gcd(ll x, ll y) { if (y == 0) { return x; } return gcd(y, x % y); // return y ? gcd(y, x%y) : x; } //ll gcd(ll x, ll y) { return y ? gcd(y, x % y) : x; } ll lcm(ll x, ll y) { return x / gcd(x, y) * y; } ll extgcd(ll x, ll y, ll& a, ll& b) { if (y == 0) { a = 1LL, b = 0LL; return x; } ll g = extgcd(y, x % y, a, b); ll ta = a, tb = b; a = tb; b = ta - x / y * tb; if (a < 0LL) a += y / g, b -= x / g; //when you wanna a >= 0 return g; } struct status { ll g, lcm, cr; }; //m(mod x), n(mod y) status crt(ll x, ll y, ll m, ll n) { status res; ll a, b; res.g = extgcd(x, y, a, b); //assume non-zero //g = xa + yb res.lcm = x / res.g * y; if ((m - n) % res.g) res.cr = -1; else {//xa'+m=-yb'+n ⇔ xa'+yb'=n-m=kg ⇔ xak+ybk = kg res.cr = (n - m) / res.g * a % (y / res.g); //係数の桁数を先に落とす res.cr = res.cr * x + m; res.cr = (res.cr % res.lcm + res.lcm) % res.lcm; } return res; } int main() { int n, m; cin >> n >> m; vi b(m), c(m); rep(i, m) cin >> b[i] >> c[i]; rep(i, m) { c[i] -= c[i] / b[i] * b[i]; if (c[i] < 0) c[i] += b[i]; } map mp; rep(i, m) { if (mp.count(b[i]) && mp[b[i]] != c[i]) { cout << "NaN" << endl; return 0; } mp[b[i]] = c[i]; } auto itr = prev(mp.end(), 1); int lb = itr->first, lc = itr->second; int ans = lc; while (ans <= n) { bool ok = true; for (auto elem : mp) { if ((ans - elem.second) % elem.first) { ok = false; break; } } if (ok) { cout << ans << endl; return 0; } ans += lb; } cout << "NaN" << endl; return 0; }