#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <deque>
#include <list>
#include <unordered_map>
#include <unordered_set>
#include <iomanip>
#include <set>
#include <map>
#include <ctime>
#include <stack>
#include <functional>
#include <cstdio>
#include <string>
#include <iostream>
#include <limits>
#include <stdexcept>
#include <numeric>
#include <fstream>
#include <atcoder/all>
#include <chrono>
#include <utility>
#include <cassert>
#include <random>
#include <stdio.h>
#include <stdlib.h>
using namespace std;
using namespace atcoder;
using namespace internal;
typedef long long ll;
typedef long double LD;
typedef double D;
typedef pair<ll,ll> P;
typedef map<ll,ll> M;
#define rep(i,n) for(ll i=0;i<n;i++)
#define rrep(i,n) for(ll i=1;i<n;i++)
#define jep(i, a, n)for (ll i =(ll)a; i<(ll)n;++i)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define fore(i,a) for(const auto &i:a)
#define all(x) (x).begin(),(x).end()
#define frac(x) x-floor(x)
#define eb emplace_back
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define SUM(x) accumulate(all(x),0)
#define uni(x) sort(all(x));x.erase(unique(all(x)),x.end())
#define TFU(s) transform(all(s),begin(s),::toupper);//大文字にする
#define TFL(s) transform(all(s),begin(s),::tolower);//小文字にする
#define replace(s,a,A) replace(s,'a','A')//str(s)のaをAにする
#define NP(a) next_permutation(all(a))
#define grid_check(a,b,h,w) (a<0 or b<0 or a>=h or b>=w)
#define ROT(s,i) rotate(s.begin(),s.begin()+i,s.end())//sのi番目から後ろを前にする
#define PQ priority_queue
#define PQD PQ<P,vector<P>,greater<P>>//小さい順に吐く
#define PQS PQ<ll,vec,greater<ll>>//大きい順に吐く
#define fi first
#define se second
#define bit(n,k) ((n>>k)&1)
#define cl clock()/CLOCKS_PER_SEC
#define printd(n,x) cout<<fixed<<setprecision(n)<<x<<endl
#define cinv(a,n); rep(i,n){cin>>a[i];}
#define cinvv(a,n,m); rep(i,n){rep(j,m){cin>>a[i][j];}}
#define popcount(n) __builtin_popcountll(n)
template<class T> inline bool chmax(T& a,T b){if(a < b){a=b;return 1;}return 0;}
template<class T> inline bool chmin(T& a,T b){if(a > b){a=b;return 1;}return 0;}
typedef vector<ll> vec;
typedef vector<vec> mat;
const LD PI=acos(-1);
//const ll mod = 1000000009;//手動で切り替える.
const ll mod = 998244353;
//const ll mod = 1000000007;
using mint =modint998244353;
//using mint =modint1000000009;
//using mint =modint1000000007;
const ll INF = (1LL<<(60));
ll dx[4]={0,1,0,-1},dy[4]={-1,0,1,0};
ll modpow(ll a,ll n,ll mod){if(mod==1)return 0;ll ret=1;ll p=a%mod;while(n){if(n&1)ret=ret*p%mod;p=p*p%mod;n>>=1;}return ret; }
M factor(ll n) {M ret;for(ll i=2;i*i<=n;i++){while(n%i==0){ret[i]++;n /= i;}}if(n != 1){ret[n]=1;}return ret;}//素因数分解
vec divisor(ll n){vec K;for(ll i=1;i*i<=n;i++){if(n%i==0){K.pb(i);if(i*i!=n)K.pb(n/i);}}sort(all(K));return K;}//約数列挙 
ll modlog(ll a,ll b,ll p){ll g=1;for(ll i=p;i;i/=2)(g*=a)%=p;g=gcd(g,p);ll t=1,c=0;for(;t%g;c++){if(t==b)return c;(t*=a)%=p;}if(b%g){return -1;}t/=g;b /= g;ll n=p/g,h=0,gs=1;for(;h*h<n; h++){(gs*=a)%=n;}unordered_map<ll,ll>bs;for(ll s=0,e=b;s<h;bs[e]=++s){(e *= a) %= n;}for(ll s = 0, e = t; s < n;){(e*=gs)%=n;s+=h;if(bs.count(e))return c+s-bs[e];}return -1;}//a^x≡b(modp) x_min //task : x=0が効かないから別の用意する
bool isprime(ll N){if(N==1){return false;}if(N==2){return true;}for(ll i=2;i*i<=N;i++){if(N%i==0)return false;}return true;}//Naiveな素数判定
static inline ll my_div(ll n, ll p) { return double(n) / p; };
ll prime_counting(ll N) {ll N2 = sqrt(N);ll NdN2 = my_div(N, N2);vec hl(NdN2);rrep(i,NdN2){hl[i] = my_div(N, i) - 1;}vec hs(N2 + 1);iota(begin(hs), end(hs), -1);for (int x = 2, pi = 0; x <= N2; ++x) {if (hs[x] == hs[x - 1]) {continue;}ll x2 = ll(x) * x;ll imax = min<ll>(NdN2, my_div(N, x2) + 1);ll ix = x;for (ll i = 1; i < imax; ++i) {hl[i] -= (ix < NdN2 ? hl[ix] : hs[my_div(N, ix)]) - pi;ix += x;}for (int n = N2; n >= x2; n--) {hs[n] -= hs[my_div(n, x)] - pi;}++pi;}return hl[1];}
mat binomial(ll n) {mat a(n+1,vec(n+1));rep(i,n+1)rep(j,i+1){if(j==0||j==i)a[i][j]=1;else a[i][j]=a[i-1][j-1]+a[i-1][j];}return a;}//O(n^2)
template<typename T>T phi(T n) {T ret=n;for(T i = 2; i * i <= n; i++){if(n % i == 0){ret -= ret / i;while(n % i == 0) n /= i;}}if(n > 1){ret -= ret / n;}return ret;}
template<typename T>T extgcd(T a, T b, T &x, T &y){T d = a;if(b != 0){d=extgcd(b,a%b,y,x);y -= (a / b) * x;}else {x = 1;y = 0;}return d;}
mat mat_mul(mat&a,mat&b){mat res(a.size(),vec(b[0].size()));rep(i,a.size()){rep(j,b[0].size()){rep(k,b.size()){(res[i][j]+=a[i][k]*b[k][j])%=mod;}}}return res;}
mat matpow(mat a,ll n){mat res(a.size(),vec(a.size()));rep(i,a.size())res[i][i]=1;while(n>0){if(n & 1)res=mat_mul(a,res);a=mat_mul(a,a);n>>=1;}return res;}
//#define mant vector<vector<mint>>//なにこれ
//mant mant_mul(mant&a,mant&b){mant res(a.size(),vector<mint>(b[0].size()));rep(i,a.size()){rep(j,b[0].size()){rep(k,b.size()){(res[i][j]+=a[i][k]*b[k][j])}}}return res;}
//mant mantpow(mant a,ll n){mant res(a.size(),vector<mint>(a.size()));rep(i,a.size())res[i][i]=1;while(n>0){if(n & 1)res=mant_mul(a,res);a=mant_mul(a,a);n>>=1;}return res;}
vec base(ll x,ll b){//(b)進数の配列を用意
vec ret;ll t = 1, k = abs(b);
while(x) {ret.emplace_back((x * t) % k);if(ret.back() < 0){ret.back() += k;}x -= ret.back() * t;x /= k;t *= b / k;}
if(ret.empty()) {ret.emplace_back(0);}reverse(begin(ret), end(ret));return ret;}
vec slide_min(const vec &v,ll k){
deque<ll> q;
vec ret;
rep(i,v.size()){
while(!q.empty() and v[q.back()]>=v[i])q.pop_back();
q.push_back(i);
if(i-k+1>=0){
ret.pb(v[q.front()]);
if(q.front()==i-k+1){q.pop_front();}
}
}
return ret;
}

struct SuccinctIndexableDictionary {size_t length;size_t blocks;vector< unsigned > bit, sum;SuccinctIndexableDictionary() = default;SuccinctIndexableDictionary(size_t length) : length(length), blocks((length + 31) >> 5) {bit.assign(blocks, 0U);sum.assign(blocks, 0U);}
void set(ll k) {bit[k >> 5] |= 1U << (k & 31);}
void build() {sum[0] = 0U;for(ll i = 1; i < blocks; i++) {sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);}}
bool operator[](ll k) {return (bool((bit[k >> 5] >> (k & 31)) & 1));}
ll rank(ll k) {return (sum[k >> 5] + __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));}
ll rank(bool val, ll k) {return (val ? rank(k) : k - rank(k));}};
template< typename T, ll MAXLOG >
struct WaveletMatrix {size_t length;SuccinctIndexableDictionary matrix[MAXLOG];ll mid[MAXLOG];WaveletMatrix() = default;WaveletMatrix(vector< T > v) : length(v.size()) {vector< T > l(length), r(length);
for(ll level = MAXLOG - 1; level >= 0; level--) {matrix[level] = SuccinctIndexableDictionary(length + 1);ll left = 0, right = 0;for(ll i = 0; i < length; i++) {if(((v[i] >> level) & 1)) {matrix[level].set(i);r[right++] = v[i];} else {l[left++] = v[i];}}
mid[level] = left;matrix[level].build();v.swap(l);for(ll i = 0; i < right; i++) {v[left + i] = r[i];}}}pair< ll, ll > succ(bool f, ll l, ll r, ll level) {
return {matrix[level].rank(f, l) + mid[level] * f, matrix[level].rank(f, r) + mid[level] * f};}
T access(ll k) {T ret = 0;for(ll level = MAXLOG - 1; level >= 0; level--) {bool f = matrix[level][k];if(f) ret |= T(1) << level;k = matrix[level].rank(f, k) + mid[level] * f;}return ret;}
T operator[](const ll &k) {return access(k);}ll rank(const T &x, ll r) {ll l = 0;for(ll level = MAXLOG - 1; level >= 0; level--) {tie(l, r) = succ((x >> level) & 1, l, r, level);}return r - l;}
T kth_smallest(ll l, ll r, ll k) {assert(0 <= k && k < r - l);T ret = 0;
for(ll level = MAXLOG - 1; level >= 0; level--) {ll cnt = matrix[level].rank(false, r) - matrix[level].rank(false, l);bool f = cnt <= k;if(f) {ret |= T(1) << level;k -= cnt;}tie(l, r) = succ(f, l, r, level);}return ret;}
T kth_largest(ll l, ll r, ll k) {return kth_smallest(l, r, r - l - k - 1);}
ll range_freq(ll l, ll r, T upper) {ll ret = 0;
for(ll level = MAXLOG - 1; level >= 0; level--) {
bool f = ((upper >> level) & 1);if(f) {ret += matrix[level].rank(false, r) - matrix[level].rank(false, l);}tie(l, r) = succ(f, l, r, level);}return ret;}
ll range_freq(ll l, ll r, T lower, T upper) {
return range_freq(l, r, upper) - range_freq(l, r, lower);}
T prev_value(ll l, ll r, T upper) {ll cnt = range_freq(l, r, upper);return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);}
T next_value(ll l, ll r, T lower) {ll cnt = range_freq(l, r, lower);return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);}};
template< typename T, ll MAXLOG >
struct CWM {WaveletMatrix< ll, MAXLOG > mat;vector< T > ys;
CWM(const vector< T > &v) : ys(v) {sort(begin(ys), end(ys));ys.erase(unique(begin(ys), end(ys)), end(ys));vec t(v.size());for(ll i = 0; i < v.size(); i++) t[i] = get(v[i]);mat = WaveletMatrix< ll, MAXLOG >(t);}
inline ll get(const T& x) {return lower_bound(begin(ys), end(ys), x) - begin(ys);}
T access(ll k) {return ys[mat.access(k)];}
T operator[](const ll &k) {return access(k);}
ll rank(const T &x, ll r) {auto pos = get(x);if(pos == ys.size() || ys[pos] != x) {return 0;}return mat.rank(pos, r);}
T kth_smallest(ll l, ll r, ll k) {return ys[mat.kth_smallest(l, r, k)];}
T kth_largest(ll l, ll r, ll k) {return ys[mat.kth_largest(l, r, k)];}
ll range_freq(ll l, ll r, T upper) {return mat.range_freq(l, r, get(upper));}
ll range_freq(ll l, ll r, T lower, T upper) {return mat.range_freq(l, r, get(lower), get(upper));}
T prev_value(ll l, ll r, T upper) {auto ret = mat.prev_value(l, r, get(upper));return ret == -1 ? T(-1) : ys[ret];}
T next_value(ll l, ll r, T lower) {auto ret = mat.next_value(l, r, get(lower));return ret == -1 ? T(-1) : ys[ret];}};
 
namespace inner { 
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
template <typename T>
T gcd(T a, T b) {
  while (b) swap(a %= b, b);
  return a;
}
template <typename T>
T inv(T a, T p) {
  T b = p, x = 1, y = 0;
  while (a) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  assert(b == 1);
  return y < 0 ? y + p : y;
}
template <typename T, typename U>
T modpow(T a, U n, T p) {
  T ret = 1 % p;
  for (; n; n >>= 1, a = U(a) * a % p)
    if (n & 1) ret = U(ret) * a % p;
  return ret;
}
}  // namespace inner
namespace my_rand {
 
// [0, 2^64 - 1)
uint64_t rng() {
  static uint64_t x_ =
      uint64_t(chrono::duration_cast<chrono::nanoseconds>(
                   chrono::high_resolution_clock::now().time_since_epoch())
                   .count()) *
      10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}
 
// [l, r)
int64_t randint(int64_t l, int64_t r) {
  assert(l < r);
  return l + rng() % (r - l);
}
 
// choose n numbers from [l, r) without overlapping
vector<int64_t> randset(int64_t l, int64_t r, int64_t n) {
  assert(l <= r && n <= r - l);
  unordered_set<int64_t> s;
  for (int64_t i = n; i; --i) {
    int64_t m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<int64_t> ret;
  for (auto& x : s) ret.push_back(x);
  return ret;
}
 
// [0.0, 1.0)
double rnd() {
  union raw_cast {
    double t;
    uint64_t u;
  };
  constexpr uint64_t p = uint64_t(1023 - 64) << 52;
  return rng() * ((raw_cast*)(&p))->t;
}
 
template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int loop = 0; loop < 2; loop++)
    for (int i = 0; i < n; i++) swap(v[i], v[randint(0, n)]);
}
 
}  // namespace my_rand
using my_rand::randint;using my_rand::randset;using my_rand::randshf;using my_rand::rnd;using my_rand::rng;
struct ArbitraryLazyMontgomeryModInt {
  using mint = ArbitraryLazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;
  static u32 mod;
  static u32 r;
  static u32 n2;
  static u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }
  static void set_mod(u32 m) {
    assert(m < (1 << 30));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u64(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }
  u32 a;
  ArbitraryLazyMontgomeryModInt() : a(0) {}
  ArbitraryLazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};
  static u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }
  mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }
  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }
  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }
 
  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }
  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = ArbitraryLazyMontgomeryModInt(t);
    return (is);
  }
  mint inverse() const { return pow(mod - 2); }
  u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }
  static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;
struct montgomery64 {
  using mint = montgomery64;
  using i64 = int64_t;
  using u64 = uint64_t;
  using u128 = __uint128_t;
  static u64 mod;
  static u64 r;
  static u64 n2;
  static u64 get_r() {
    u64 ret = mod;
    for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
    return ret;
  }
  static void set_mod(u64 m) {
    assert(m < (1LL << 62));
    assert((m & 1) == 1);
    mod = m;
    n2 = -u128(m) % m;
    r = get_r();
    assert(r * mod == 1);
  }
  u64 a;
  montgomery64() : a(0) {}
  montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};
  static u64 reduce(const u128 &b) {
    return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
  }
  mint &operator+=(const mint &b) {
    if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator-=(const mint &b) {
    if (i64(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }
  mint &operator*=(const mint &b) {
    a = reduce(u128(a) * b.a);
    return *this;
  }
  mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }
  mint operator+(const mint &b) const { return mint(*this) += b; }
  mint operator-(const mint &b) const { return mint(*this) -= b; }
  mint operator*(const mint &b) const { return mint(*this) *= b; }
  mint operator/(const mint &b) const { return mint(*this) /= b; }
  bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  mint operator-() const { return mint() - mint(*this); }
  mint pow(u128 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }
  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = montgomery64(t);
    return (is);
  }
  mint inverse() const { return pow(mod - 2); }
  u64 get() const {
    u64 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }
  static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;
namespace fast_factorize {
using u64 = uint64_t;
template <typename mint>
bool miller_rabin(u64 n, vector<u64> as) {
  if (mint::get_mod() != n) mint::set_mod(n);
  u64 d = n - 1;
  while (~d & 1) d >>= 1;
  mint e{1}, rev{int64_t(n - 1)};
  for (u64 a : as) {
    if (n <= a) break;
    u64 t = d;
    mint y = mint(a).pow(t);
    while (t != n - 1 && y != e && y != rev) {
      y *= y;
      t *= 2;
    }
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}
bool is_prime(u64 n) {
  if (~n & 1) return n == 2;
  if (n <= 1) return false;
  if (n < (1LL << 30))
    return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
  else
    return miller_rabin<montgomery64>(
        n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
template <typename mint, typename T>
T pollard_rho(T n) {
  if (~n & 1) return 2;
  if (is_prime(n)) return n;
  if (mint::get_mod() != n) mint::set_mod(n);
  mint R, one = 1;
  auto f = [&](mint x) { return x * x + R; };
  auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
  while (1) {
    mint x, y, ys, q = one;
    R = rnd_(), y = rnd_();
    T g = 1;
    constexpr int m = 128;
    for (int r = 1; g == 1; r <<= 1) {
      x = y;
      for (int i = 0; i < r; ++i) y = f(y);
      for (int k = 0; g == 1 && k < r; k += m) {
        ys = y;
        for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
        g = inner::gcd<T>(q.get(), n);
      }
    }
    if (g == n) do
        g = inner::gcd<T>((x - (ys = f(ys))).get(), n);
      while (g == 1);
    if (g != n) return g;
  }
  exit(1);
}
using i64 = long long;
vector<i64> inner_factorize(u64 n) {
  if (n <= 1) return {};
  u64 p;
  if (n <= (1LL << 30))
    p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
  else
    p = pollard_rho<montgomery64, uint64_t>(n);
  if (p == n) return {i64(p)};
  auto l = inner_factorize(p);
  auto r = inner_factorize(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}
vector<i64> factorize(u64 n) {
  auto ret = inner_factorize(n);
  sort(begin(ret), end(ret));
  return ret;
}
map<i64, i64> factor_count(u64 n) {
  map<i64, i64> mp;
  for (auto &x : factorize(n)) mp[x]++;
  return mp;
}
vector<i64> divisors(u64 n) {
  if (n == 0) return {};
  vector<pair<i64, i64>> v;
  for (auto &p : factorize(n)) {
    if (v.empty() || v.back().first != p) {
      v.emplace_back(p, 1);
    } else {
      v.back().second++;
    }
  }
  vector<i64> ret;
  auto f = [&](auto rc, int i, i64 x) -> void {
    if (i == (int)v.size()) {
      ret.push_back(x);
      return;
    }
    for (int j = v[i].second;; --j) {
      rc(rc, i + 1, x);
      if (j == 0) break;
      x *= v[i].first;
    }
  };
  f(f, 0, 1);
  sort(begin(ret), end(ret));
  return ret;
}
 
}  // namespace fast_factorize
using fast_factorize::divisors;using fast_factorize::factor_count;using fast_factorize::factorize;using fast_factorize::is_prime;
using namespace fast_factorize;

struct Barrett {
  using u32 = unsigned int;
  using i64 = long long;
  using u64 = unsigned long long;
  u32 m;
  u64 im;
  Barrett() : m(), im() {}
  Barrett(int n) : m(n), im(u64(-1) / m + 1) {}
  constexpr inline i64 quo(u64 n) {
    u64 x = u64((__uint128_t(n) * im) >> 64);
    u32 r = n - x * m;
    return m <= r ? x - 1 : x;
  }
  constexpr inline i64 rem(u64 n) {
    u64 x = u64((__uint128_t(n) * im) >> 64);
    u32 r = n - x * m;
    return m <= r ? r + m : r;
  }
  constexpr inline pair<i64, int> quorem(u64 n) {
    u64 x = u64((__uint128_t(n) * im) >> 64);
    u32 r = n - x * m;
    if (m <= r) return {x - 1, r + m};
    return {x, r};
  }
  constexpr inline i64 pow(u64 n, i64 p) {
    u32 a = rem(n), r = m == 1 ? 0 : 1;
    while (p) {
      if (p & 1) r = rem(u64(r) * a);
      a = rem(u64(a) * a);
      p >>= 1;
    }
    return r;
  }
};
struct prime_power_binomial {
  int p, q, M;
  vector<int> fac, ifac, inv;
  int delta;
  Barrett bm, bp;
 
  prime_power_binomial(int _p, int _q) : p(_p), q(_q) {
    assert(1 < p && p <= ((1LL << 30) - 1));
    assert(_q > 0);
    long long m = 1;
    while (_q--) {
      m *= p;
      assert(m <=((1LL << 30) - 1));
    }
    M = m;
    bm = Barrett(M), bp = Barrett(p);
    enumerate();
    delta = (p == 2 && q >= 3) ? 1 : M - 1;
  }
 
  void enumerate() {
    int MX = min<int>(M, 20000000 + 10);
    fac.resize(MX);
    ifac.resize(MX);
    inv.resize(MX);
    fac[0] = ifac[0] = inv[0] = 1;
    fac[1] = ifac[1] = inv[1] = 1;
    for (int i = 2; i < MX; i++) {
      if (i % p == 0) {
        fac[i] = fac[i - 1];
        fac[i + 1] = bm.rem(1LL * fac[i - 1] * (i + 1));
        i++;
      } else {
        fac[i] = bm.rem(1LL * fac[i - 1] * i);
      }
    }
    ifac[MX - 1] = bm.pow(fac[MX - 1], M / p * (p - 1) - 1);
    for (int i = MX - 2; i > 1; --i) {
      if (i % p == 0) {
        ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1));
        ifac[i - 1] = ifac[i];
        i--;
      } else {
        ifac[i] = bm.rem(1LL * ifac[i + 1] * (i + 1));
      }
    }
  }
 
  long long Lucas(long long n, long long m) {
    int res = 1;
    while (n) {
      int n0, m0;
      tie(n, n0) = bp.quorem(n);
      tie(m, m0) = bp.quorem(m);
      if (n0 < m0) return 0;
      res = bm.rem(1LL * res * fac[n0]);
      int buf = bm.rem(1LL * ifac[n0 - m0] * ifac[m0]);
      res = bm.rem(1LL * res * buf);
    }
    return res;
  }
 
  long long C(long long n, long long m) {
    if (n < m || n < 0 || m < 0) return 0;
    if (q == 1) return Lucas(n, m);
    long long r = n - m;
    int e0 = 0, eq = 0, i = 0;
    int res = 1;
    while (n) {
      res = bm.rem(1LL * res * fac[bm.rem(n)]);
      res = bm.rem(1LL * res * ifac[bm.rem(m)]);
      res = bm.rem(1LL * res * ifac[bm.rem(r)]);
      n = bp.quo(n);
      m = bp.quo(m);
      r = bp.quo(r);
      int eps = n - m - r;
      e0 += eps;
      if (e0 >= q) return 0;
      if (++i >= q) eq += eps;
    }
    if (eq & 1) res = bm.rem(1LL * res * delta);
    res = bm.rem(1LL * res * bm.pow(p, e0));
    return res;
  }
};
struct binomial_mod {
  int mod;
  vector<int> M;
  vector<prime_power_binomial> cs;
 
  binomial_mod(long long md) : mod(md) {
    assert(1 <= md);
    assert(md <= ((1LL << 30) - 1));
    for (int i = 2; i * i <= md; i++) {
      if (md % i == 0) {
        int j = 0, k = 1;
        while (md % i == 0) md /= i, j++, k *= i;
        M.push_back(k);
        cs.emplace_back(i, j);
        assert(M.back() == cs.back().M);
      }
    }
    if (md != 1) {
      M.push_back(md);
      cs.emplace_back(md, 1);
    }
    assert(M.size() == cs.size());
  }
 
  long long binom(long long n, long long m) {
    if (mod == 1) return 0;
    vector<long long> rem, d;
    for (int i = 0; i < (int)cs.size(); i++) {
      rem.push_back(cs[i].C(n, m));
      d.push_back(M[i]);
    }
    return atcoder::crt(rem, d).first;
  }
};


#define is_prime(x) is_prime_constexpr(x)


//FPS!!
ll modPow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
ll modsqrt(ll a,ll mod){
  if(mod==2||a==0) return a;
  if(modPow(a,(mod-1)/2,mod)!=1) return -1;
  if(mod%4==3) return modPow(a,(mod+1)/4,mod);
  ll q=mod-1;
  ll s=0;
  while(q%2==0){
    q/=2;
    s++;
  }
  ll z=1;
  random_device rnd;
  while(modPow(z=rnd()%mod,(mod-1)/2,mod)!=mod-1);
  ll c=modPow(z,q,mod),t=modPow(a,q,mod),r=modPow(a,(q+1)/2,mod),m=s;
  while(m>1){
    if(modPow(t,1<<(m-2),mod)==1){
      c*=c;
      c%=mod;
      m--;
    }
    else{
      tie(c,t,r,m)=make_tuple(c*c%mod,c*c%mod*t%mod,c*r%mod,m-1);
    }
  }
  return r%mod;
}
template<class T>
struct FormalPowerSeries:vector<T>{
  using vector<T>::vector;
  using vector<T>::operator=;
  using F = FormalPowerSeries;
  
  F operator-() const{
    F res(*this);
    for(auto &e:res) e=-e;
    return res;
  }
  F &operator*=(const T &g){
    for(auto &e:*this) e*=g;
    return *this;
  }
  F &operator/=(const T &g){
    assert(g!=T(0));
    *this*=g.inv();
    return *this;
  }
  F &operator+=(const F &g){
    int n=(*this).size(),m=g.size();
    for(int i=0;i<min(n,m);i++){
      (*this)[i]+=g[i];
    }
    return *this;
  }
  F &operator-=(const F &g){
    int n=(*this).size(),m=g.size();
    for(int i=0;i<min(n,m);i++){
      (*this)[i]-=g[i];
    }
    return *this;
  }
  F &operator<<=(const int d) {
    int n=(*this).size();
    (*this).insert((*this).begin(),d,0);
    (*this).resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n=(*this).size();
    (*this).erase((*this).begin(),(*this).begin()+min(n, d));
    (*this).resize(n);
    return *this;
  }
  F inv(int d=-1) const{
    int n=(*this).size();
    assert(n!=0&&(*this)[0]!=0);
    if(d==-1) d=n;
    assert(d>0);
    F res{(*this)[0].inv()};
    while(res.size()<d){
      int m=size(res);
      F f(begin(*this),begin(*this)+min(n,2*m));
      F r(res);
      f.resize(2*m);
      r.resize(2*m);
      vector<T> s=convolution(f,r);
      s.resize(2*m);
      for(int i=0;i<2*m;i++){
        s[i]=-s[i];
      }
      s[0]+=2;
      vector<T> g=convolution(s,r);
      g.resize(2*m);
      res=g;
    }
    res.resize(n);
    return res;
  }
  F &operator*=(const F &g){
    int n=(*this).size();
    *this=convolution(*this,g);
    (*this).resize(n);
    return (*this);
  }
  F &operator/=(const F &g){
    int n=(*this).size();
    *this=convolution(*this,g.inv());
    (*this).resize(n);
    return (*this);
  }
  void onemultiply(const int d,const T c){
    int n=(*this).size();
    for(int i=n-d-1;i>=0;i--){
      (*this)[i+d]+=(*this)[i]*c;
    }
  }
  void onediv(const int d,const T c){
    int n=(*this).size();
    for(int i=n-d-1;i>=0;i--){
      (*this)[i+d]-=(*this)[i]*c;
    }
  }
  T eval(const T &a) const {
    T x(1),res(0);
    for(auto e:*this) res+=e*x,x*=a;
    return res;
  }
  F differential() const {
    int n=(*this).size();
    F res(n);
    for(int i=0;i<n-1;i++){
      res[i]=T(i+1)*(*this)[i+1];
    }
    res[n-1]=0;
    return res;
  }
  F Integral() const {
    int n=(*this).size();
    F res(n);
    for(int i=1;i<n;i++){
      res[i]=(*this)[i-1]/T(i);
    }
    res[0]=0;
    return res;
  }
  F log() const{
    assert((*this)[0]==1);
    int n=(*this).size();
    F u=(*this).differential();
    F d=(*this);
    u/=d;
    u=u.Integral();
    u.resize(n);
    return u;
  }
  F exp(ll d=-1) const{
    ll n=(*this).size();
    assert(n!=0&&(*this)[0]==0);
    if(d==-1) d=n;
    assert(d>0);
    F res{1};
    while(res.size()<d){
      ll m=size(res);
      F f(begin(*this),begin(*this)+min(n,2*m));
      F r(res);
      f.resize(2*m);
      r.resize(2*m);
      r=r.log();
      f-=r;
      f[0]++;
      F g=f*res;
      g.resize(2*m);
      res=g;
    }
    res.resize(n);
    return res;
  }
  F pow(ll a){
    ll n=(*this).size();
    F res(n);
    for(ll i=0;i<n;i++){
      res[i]=(*this)[i];
    }
    if(a==0){
      F s(n);
      if(n>0){
        s[0]=T(1);
      }
      for(ll i=0;i<n;i++){
      res[i]=s[i];
      }
      return res;
    }
    int l=0;
    while(l<n&&res[l]==0) l++;
    if(l>(n-1)/a||l==n){
      F s(n);
      for(ll i=0;i<n;i++){
        res[i]=s[i];
      }
      return res;
    }
    T t=res[l];
    res.erase(res.begin(),res.begin()+l);
    res/=t;
    F g=res.log();
    for(ll i=0;i<n;i++){
      res[i]=g[i];
    }
    res*=a;
    g=res.exp();
    for(ll i=0;i<n;i++){
      res[i]=g[i];
    }
    res*=t.pow(a);
    res.insert(res.begin(),l*a,0);
    return res;
  }
  F sqrt(int k=-1){
    int n=(*this).size();
    if(k==-1){
      k=n;
    }
    ll m=T::mod();
    if((*this)[0]==T(0)){
      for(int i=1;i<int((*this).size());i++){
        if((*this)[i]!=T(0)){
          if(i&1) return {};
          if(n-i/2<=0)break;
          auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
          if(int(ret.size())<n) return {};
          return ret;
        }
      }
      F g(n);
      for(int i=0;i<n;i++){
        g[i]=0;
      }
      return g;
    }
    else{
      if(modsqrt((*this)[0].val(),m)==-1){
        return {};
      }
      F ret{T(modsqrt((*this)[0].val(),m))};
      for(int i=1;i<n;i<<=1){
        ret.resize(2*i);
        ret=(ret+(*this)/ret);
        ret/=T(2);
      }
      return ret;
    }
  }
  pair<F,F> division(F g){
    F f=(*this);
    int n=f.size();
    int m=g.size();
    if(n<m){
      F p(0);
      return {p,f};
    }
    F p(n-m+1),q(n-m+1);
    for(int i=0;i<n-m+1;i++) p[i]=f[n-i-1];
    for(int i=0;i<n-m+1&&i<m;i++) q[i]=g[m-i-1];
    p/=q;
    for(int i=0;i<(n-m+1)/2;i++) swap(p[i],p[(n-m+1)-i-1]);
    g.resize(n);
    g*=p;
    for(int i=0;i<n;i++) f[i]-=g[i];
    int v=n-m+1,u=0;
    for(int i=0;i<n;i++) if(f[i].val()) chmax(u,i+1);
    p.resize(v);
    f.resize(u);
    return {p,f};
  } 
  F operator*(const T &g) const { return F(*this)*=g;}
  F operator-(const T &g) const { return F(*this)-=g;}
  F operator*(const F &g) const { return F(*this)*=g;}
  F operator-(const F &g) const { return F(*this)-=g;}
  F operator+(const F &g) const { return F(*this)+=g;}
  F operator/(const F &g) const { return F(*this)/=g;}
  F operator<<(const int d) const { return F(*this)<<=d;}
  F operator>>(const int d) const { return F(*this)>>=d;}  
};
using fps = FormalPowerSeries<mint>;
fps partition(ll N) {
fps po(N + 1);
po[0] = 1;
rrep(k,N+1){
if(1LL * k * (3 * k + 1) / 2 <= N) po[k * (3 * k + 1) / 2] += (k % 2 ? -1 : 1);
if(1LL * k * (3 * k - 1) / 2 <= N) po[k * (3 * k - 1) / 2] += (k % 2 ? -1 : 1);
}
return po.inv();
}







int main(){
ll n;
cin>>n;
ll m;
cin>>m;
cout << (n*(n+1)<=2*m ? "Yes" : "No") <<endl;
}