#pragma region MACROS

#pragma region HEADER
#pragma GCC optimize("O3")
#ifdef LOCAL
#include "utility/debug_print.hpp"
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
#include <bits/stdc++.h>
#include <immintrin.h>
using namespace std;
#define endl '\n'
#pragma endregion
#pragma region TYPES
using ll = long long;
using pii = pair<ll, ll>;
using ld = long double;
template <typename T>
using vc = vector<T>;
template <typename T>
using vvc = vector<vc<T>>;
template <typename T>
using vvvc = vector<vvc<T>>;
using vi = vc<int>;
using vvi = vvc<int>;
using vvvi = vvvc<int>;
using vpi = vc<pii>;
using vvpi = vvc<pii>;
using vvvpi = vvvc<pii>;
using vb = vc<bool>;
using vvb = vvc<bool>;
using vvvb = vvvc<bool>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#pragma endregion
#pragma region UTILITY_FUNCTIONS
template <typename T>
int si(const T& x) { return x.size(); }
template <typename T, typename S>
inline bool chmax(T& a, const S& b) { return (a < b ? a = b, 1 : 0); }
template <typename T, typename S>
inline bool chmin(T& a, const S& b) { return (a > b ? a = b, 1 : 0); }
#define overload2(a, b, name, ...) name
#define overload4(a, b, c, d, name, ...) name
#define overload5(a, b, c, d, e, name, ...) name
#pragma endregion
#pragma region WORDS
#define fi first
#define se second
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define eb emplace_back
#define ef emplace_front
#pragma endregion
#pragma region LOOPS
#define rep0(n) for (int _ = 0; _ < n; ++_)
#define rep1(i, n) for (ll i = 0; i < (n); ++i)
#define rep2(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep3(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rrep0(n) for (int jidlsjf = 0; jidlsjf < n; ++jidlsjf)
#define rrep1(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep2(i, a, b) for (ll i = (a)-1; i >= b; --i)
#define rrep3(i, a, b, c) for (ll i = (a)-1; i >= b; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep3, rrep2, rrep1, rrep0)(__VA_ARGS__)
#define fore0(v) rep(a.size())
#define fore1(a, v) for (auto&& a : v)
#define fore2(a, b, v) for (auto&& [a, b] : v)
#define fore3(a, b, c, v) for (auto&& [a, b, c] : v)
#define fore4(a, b, c, d, v) for (auto&& [a, b, c, d] : v)
#define fore(...) overload5(__VA_ARGS__, fore4, fore3, fore2, fore1, fore0)(__VA_ARGS__)
#pragma endregion
#pragma region CONTAINER_METHODS
#define all(c) begin(c), end(c)
#define rall(c) rbegin(c), rend(c)
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define fi_geq(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define la_l(c, x) distance((c).begin(), lower_bound(all(c), (x))) - 1
#define la_leq(c, x) distance((c).begin(), upper_bound(all(c), (x))) - 1
#define fi_g(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define fi_leq(c, x) distance((c).begin(), lower_bound(all(c), (x), greater<ll>()))
#define la_g(c, x) distance((c).begin(), lower_bound(all(c), (x), greater<ll>())) - 1
#define la_geq(c, x) distance((c).begin(), upper_bound(all(c), (x), greater<ll>())) - 1
#define fi_l(c, x) distance((c).begin(), upper_bound(all(c), (x), greater<ll>()))
#define SORT(v) sort(all(v))
#define REV(v) reverse(all(v))
#define UNIQUE(x) SORT(x), x.erase(unique(all(x)), x.end())
template <typename T = ll, typename S>
T SUM(const S& v) { return accumulate(all(v), T(0)); }
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define ARGMAX(v) distance((v).begin(), max_element(all(v)))
#define ARGMIN(v) distance((v).begin(), min_element(all(v)))
template <typename T = int>
T mex(unordered_set<T> st) {
  T ret = T(0);
  while (st.count(ret) != 0) ++ret;
  return ret;
}
#pragma endregion
#pragma region VECTOR_DEFINITIONS
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vec2(type, name1, name2, ...) vector<type> name1(__VA_ARGS__), name2(__VA_ARGS__)
#define vec3(type, name1, name2, name3, ...) vector<type> name1(__VA_ARGS__), name2(__VA_ARGS__), name3(__VA_ARGS__)
#define vec4(type, name1, name2, name3, name4, ...) vector<type> name1(__VA_ARGS__), name2(__VA_ARGS__), name3(__VA_ARGS__), name4(__VA_ARGS__)
#define vv(type, name, a, ...) vector<vector<type>> name(a, vector<type>(__VA_ARGS__))
#define vvv(type, name, a, b, ...) vector<vector<vector<type>>> name(a, vector<vector<type>>(b, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};
constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
vi iota(int n) {
  vi a(n);
  return iota(a.begin(), a.end(), 0), a;
}
template <typename T>
vi iota(const vector<T> &a, bool greater = false) {
  vi res(a.size());
  iota(res.begin(), res.end(), 0);
  sort(res.begin(), res.end(), [&](int i, int j) {
    if (greater) return a[i] > a[j];
    return a[i] < a[j];
  });
  return res;
}
#pragma endregion
#pragma region TYPICAL_OUTPUT
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { cout << yesno[t] << endl; }
void no(bool t = 1) { yes(!t); }
#pragma endregion
#pragma region INPUT
int scan() { return getchar(); }
void scan(signed& a) { cin >> a; }
void scan(long long& a) { cin >> a; }
void scan(char& a) { cin >> a; }
void scan(double& a) { cin >> a; }
void scan(string& a) { cin >> a; }
template <class T, class S>
void scan(pair<T, S>& p) { scan(p.first), scan(p.second); }
template <class T>
void scan(vector<T>& a) {
  for (auto& i : a) scan(i);
}
template <class T>
void scan(T& a) { cin >> a; }
void IN() {}
template <class Head, class... Tail>
void IN(Head& head, Tail&... tail) {
  scan(head);
  IN(tail...);
}
#define INT(...)   \
  int __VA_ARGS__; \
  IN(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  IN(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  IN(__VA_ARGS__)
#define CHR(...)    \
  char __VA_ARGS__; \
  IN(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  IN(__VA_ARGS__)
#define VEC(type, name, size) \
  vector<type> name(size);    \
  IN(name)
#define VEC2(type, name1, name2, size)   \
  vector<type> name1(size), name2(size); \
  for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)         \
  vector<type> name1(size), name2(size), name3(size); \
  for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)               \
  vector<type> name1(size), name2(size), name3(size), name4(size); \
  for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i])
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  IN(name)
#pragma endregion
#pragma region MATH
ll max(signed a, ll b) { return max(ll(a), b); }
ll max(ll a, signed b) { return max(a, ll(b)); }
ll min(signed a, ll b) { return min(ll(a), b); }
ll min(ll a, signed b) { return min(a, ll(b)); }
static constexpr ll inf = numeric_limits<ll>::max() / 2;
// static constexpr ll infll = numeric_limits<ll>::max() / 2;
static constexpr double infdbl = numeric_limits<double>::max() / 2;
template <typename T, typename S>
T ceil(T x, S y) {
  assert(y);
  return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
template <typename T, typename S>
T floor(T x, S y) {
  assert(y);
  return (y < 0 ? floor(-x, -y)
                : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
ll POW(ll x, ll n) {
  ll ret = 1;
  for (; n; n >>= 1, x *= x)
    if (n & 1) ret *= x;
  return ret;
}
ll POW(ll x, ll n, const int mod) {
  ll ret = 1;
  x %= mod;
  for (; n; n >>= 1, x = x * x % mod)
    if (n & 1) ret = ret * x % mod;
  return ret;
}
template <typename T>
map<T, int> factor(T n) {
  map<T, int> ret;
  for (T i = 2; i * i <= n; i++) {
    while (n % i == 0) {
      ret[i]++;
      n /= i;
    }
  }
  if (n != 1) ret[n] = 1;
  return ret;
}
template <class T>
vector<T> divisor(T x) {
  vector<T> ret;
  for (T i = 1; i * i <= x; i++)
    if (x % i == 0) {
      ret.pb(i);
      if (i * i != x) ret.pb(x / i);
    }
  return ret;
}
vector<int> cumsum(const vector<bool>& v) {
  vector<int> ret(v.size());
  for (int i = 0; i < (int)v.size(); ++i) ret[i] = (i == 0 ? 0 : ret[i - 1]) + v[i];
  return ret;
}
template <typename T>
vector<T> cumsum(const vector<T>& v) {
  vector<T> ret(v.size());
  for (int i = 0; i < (int)v.size(); ++i) ret[i] = (i == 0 ? 0 : ret[i - 1]) + v[i];
  return ret;
}
template <typename T>
vector<vector<T>> cumsum2d(const vector<vector<T>>& v) {
  vector<vector<T>> ret = v;
  for (int i = 0; i < (int)v.size(); ++i) {
    for (int j = 0; j < (int)v[0].size(); ++j) {
      if (i > 0) ret[i][j] += ret[i - 1][j];
      if (j > 0) ret[i][j] += ret[i][j - 1];
      if (i > 0 && j > 0) ret[i][j] -= ret[i - 1][j - 1];
    }
  }
  return ret;
}
template <typename T>
T parsum2d(const vector<vector<T>>& cum, int i1, int i2, int j1, int j2) {
  if (i1 > i2 || j1 > j2) return 0;
  T ret = cum[i2][j2];
  if (i1 > 0) ret -= cum[i1 - 1][j2];
  if (j1 > 0) ret -= cum[i2][j1 - 1];
  if (i1 > 0 && j1 > 0) ret += cum[i1 - 1][j1 - 1];
  return ret;
}
template <typename T, typename S, typename U>
bool inc(const T& x, const S& l, const U& r) {
  return l <= x and x < r;
}
constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
template <typename T>
T arith_sum_from_range(T first, T last, T diff = T(1)) {
  assert((last - first) % diff == 0);
  return ((last - first) / 2 + 1) * (first + last) / 2;
}
template <typename T, typename S>
T arith_sum_from_term(T first, S n, T diff = T(1)) {
  return (2 * first + (n - 1) * diff) * n / 2;
}
#pragma endregion
#pragma region BIT_FUNCTIONS
ll pow2(int i) { return 1LL << i; }
#define bit(n, k) (((n) >> (k)) & 1)
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
constexpr ll mask(int n) { return (1LL << n) - 1; }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
template <typename T>
T inv_all_bit(T a) {
  T ret = 0;
  int n = topbit(a);
  rep(i, n) if (((a >> i) & 1) == 0) ret += (1 << i);
  return ret;
}
template <typename T>
T inv_all_bit(T a, int n) {
  T ret = 0;
  rep(i, n) if (((a >> i) & 1) == 0) ret += (1 << i);
  return ret;
}
template <typename T>
T inv_bit(T a, int k) { return a ^ (1 << k); }
template <typename T>
bool checkbit(T a, int shift) { return ((a >> shift) & 1) == 1; }
#pragma endregion
#pragma region PAIR_OPERATORS
template <class T, class S>
pair<T, S> operator-(const pair<T, S>& x, const pair<T, S>& y) {
  return pair<T, S>(x.fi - y.fi, x.se - y.se);
}
template <class T, class S>
pair<T, S> operator+(const pair<T, S>& x, const pair<T, S>& y) {
  return pair<T, S>(x.fi + y.fi, x.se + y.se);
}
template <class T>
pair<T, T> operator&(const pair<T, T>& l, const pair<T, T>& r) {
  return pair<T, T>(max(l.fi, r.fi), min(l.se, r.se));
}
template <class T, class S>
pair<T, S> operator+=(pair<T, S>& l, const pair<T, S>& r) {
  return l = l + r;
}
template <class T, class S>
pair<T, S> operator-=(pair<T, S>& l, const pair<T, S>& r) {
  return l = l - r;
}
template <class T>
bool intersect(const pair<T, T>& l, const pair<T, T>& r) {
  return (l.se < r.se ? r.fi < l.se : l.fi < r.se);
}
#pragma endregion
#pragma region SEARCH
template <class F>
void bit_search(int n, const F& f) {
  for (int i = 0; i < (1 << n); ++i) {
    set<int> st;
    for (int j = 0; j < n; ++j) {
      if ((i >> j & 1) == 1) {
        st.insert(j);
      }
    }
    f(st);
  }
}
template <typename S, typename T, class F>
ll bin_search(S ok, T ng, const F& f) {
  ll _ok = ok, _ng = ng;
  while (abs(_ok - _ng) > 1) {
    ll mid = (_ok + _ng) >> 1;
    (f(mid) ? _ok : _ng) = mid;
  }
  return _ok;
}
template <typename S, typename T, class F>
double bin_search_double(S ok, T ng, const F& f, int iter = 80) {
  double _ok = ok, _ng = ng;
  while (iter--) {
    double mid = (_ok + _ng) / 2;
    (f(mid) ? _ok : _ng) = mid;
  }
  return _ok;
}
#pragma endregion
#pragma region STRING
void ERASE(string& s, char c) { s.erase(remove(all(s), c), s.end()); }
void ERASE(string& s, const string& chars) { fore(c, chars) s.erase(remove(all(s), c), s.end()); }
void ERASE(string& s, const vector<char>& chars) { fore(c, chars) s.erase(remove(all(s), c), s.end()); }
template <typename T>
void ERASE(vector<T>& v, T x) { v.erase(remove(all(v), x), v.end()); }
template <typename T>
void ERASE(vector<T>& v, const vector<T>& list) { fore(x, list) v.erase(remove(all(v), x), v.end()); }
#pragma endregion
#pragma region OUTPUT
template <typename T, typename S>
ostream& operator<<(ostream& os, const pair<T, S>& p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (((i + 1) != v.size()) ? " " : "");
  }
  return os;
}
void OUT() { cout << endl; }
template <class Head, class... Tail>
void OUT(const Head& head, const Tail&... tail) {
  cout << head;
  if (sizeof...(tail)) cout << ' ';
  OUT(tail...);
}
template <typename T>
string pad(T n, int d, char c) {
  ostringstream sout;
  sout << setfill(c) << setw(d) << n;
  return sout.str();
}
#pragma endregion
#pragma region GRAPH
template <typename T = ll>
struct Edge {
  int from, to;
  T cost;
  int id;

  Edge() = default;
  Edge(int from, int to, T cost = 1, int id = -1) : from(from), to(to), cost(cost), id(id) {}

  operator int() const {
    return to;
  }
};

template <typename T = ll>
struct Graph {
  vector<vector<Edge<T>>> g;
  int edge_id;

  Graph() = default;
  explicit Graph(int n) : g(n), edge_id(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, edge_id++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, edge_id);
    g[to].emplace_back(to, from, cost, edge_id++);
  }

  void read(int m, int padding = -1, bool weighted = false, bool directed = false) {
    for (int i = 0; i < m; ++i) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed) add_directed_edge(a, b, c);
      else add_edge(a, b, c);
    }
  }

  inline vector<Edge<T>> &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T>> &operator[](const int &k) const { return g[k]; }
};
#pragma endregion
#pragma region PARSE
inline int toi(char c) { return c - '0'; }
int toi(string s) { return stoi(s); }
ll toll(string s) { return stoll(s); }
template <typename T>
string tos(T x) {
  return to_string(x);
}
inline char toc(int i) { return '0' + i; }
template <typename T>
string tobit(T x, size_t d) {
  if (d <= 2)
    return bitset<2>(x).to_string();
  else if (d <= 4)
    return bitset<4>(x).to_string();
  else if (d <= 8)
    return bitset<8>(x).to_string();
  else if (d <= 16)
    return bitset<16>(x).to_string();
  else if (d <= 32)
    return bitset<32>(x).to_string();
  else
    return bitset<64>(x).to_string();
}
#pragma endregion

#pragma region MOD
template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;
  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }
  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(r * mod == 1, "invalid, r * mod != 1");
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  u32 a;
  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};
  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }
  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }
  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }
  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }
  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }
  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  constexpr mint inverse() const { return pow(mod - 2); }
  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 = LazyMontgomeryModInt<mod>(t);
    return (is);
  }
  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }
  static constexpr u32 get_mod() { return mod; }
};
__attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(
    const __m128i &a, const __m128i &b) {
  return _mm_mullo_epi32(a, b);
}
__attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(
    const __m128i &a, const __m128i &b) {
  __m128i a13 = _mm_shuffle_epi32(a, 0xF5);
  __m128i b13 = _mm_shuffle_epi32(b, 0xF5);
  __m128i prod02 = _mm_mul_epu32(a, b);
  __m128i prod13 = _mm_mul_epu32(a13, b13);
  __m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
                                    _mm_unpackhi_epi32(prod02, prod13));
  return prod;
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(
    const __m128i &a, const __m128i &b, const __m128i &r, const __m128i &m1) {
  return _mm_sub_epi32(
      _mm_add_epi32(my128_mulhi_epu32(a, b), m1),
      my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(
    const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
  __m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
  return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(
    const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
  __m128i ret = _mm_sub_epi32(a, b);
  return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}
__attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(
    const __m256i &a, const __m256i &b) {
  return _mm256_mullo_epi32(a, b);
}
__attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(
    const __m256i &a, const __m256i &b) {
  __m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
  __m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
  __m256i prod02 = _mm256_mul_epu32(a, b);
  __m256i prod13 = _mm256_mul_epu32(a13, b13);
  __m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
                                       _mm256_unpackhi_epi32(prod02, prod13));
  return prod;
}
__attribute__((target("avx2"))) inline __m256i montgomery_mul_256(
    const __m256i &a, const __m256i &b, const __m256i &r, const __m256i &m1) {
  return _mm256_sub_epi32(
      _mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
      my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}
__attribute__((target("avx2"))) inline __m256i montgomery_add_256(
    const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
  __m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
  return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                          ret);
}
__attribute__((target("avx2"))) inline __m256i montgomery_sub_256(
    const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
  __m256i ret = _mm256_sub_epi32(a, b);
  return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                          ret);
}
#pragma endregion
#pragma endregion
using mint = LazyMontgomeryModInt<1000000007>;
// using mint = LazyMontgomeryModInt<998244353>;
using vmi = vc<mint>;
using vvmi = vvc<mint>;
using vvvmi = vvvc<mint>;
#define int ll

//
//
//

// #include "./solve.cpp"
void solve() {
  INT(n, x, y);
  VEC(int, r, n);
  SORT(r);
  if(n == 1 && x * x + y * y != r[0] * r[0]) {
    No();
    return;
  }
  int tot = 0;
  tot += r[0];
  rep(i, 1, n) tot += 2 * r[i];
  if(x * x + y * y <= tot * tot) Yes();
  else No();
}
//
//
//

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << fixed << setprecision(9);
  cerr << fixed << setprecision(9);

  // INT(t);
  int t = 1;

  while (t--) {
    solve();
  }

  return 0;
}