#pragma region Macros
#pragma comment(linker, "/stack:200000000")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,fma,abm,mmx,avx,avx2,tune=native")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,fma,abm,mmx,avx,avx2")
// #pragma GCC target("avx2")
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#define ll long long
using ld = long double;
#define rep2(i, a, b) for(ll i = (a); i <= (b); i++)
#define rep3(i, a, b) for(ll i = (a); i >= (b); --i)
#define rep(i, n) for(ll i = 0; i < n; ++i)
#define pii pair<int, int>
#define pll pair<ll, ll>
#define pb push_back
#define eb emplace_back
#define vi vector<int>
#define vll vector<ll>
#define vpi vector<pii>
#define vpll vector<pll>
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__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 vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                                                                                                   \
    vector<vector<type>> name(h, vector<type>(w));                                                                                                             \
    IN(name)
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, 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__))))
#define mt make_tuple
#define fi first
#define se second
#define all(c) begin(c), end(c)
#define SORT(v) sort(all(v))
#define REV(v) reverse(all(v))
template <class T = ll, class S> T SUM(const std::vector<S> &v) { return accumulate(all(v), T(0)); }
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
using namespace std;
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}};
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); }
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
#define si(c) (int)(c).size()
#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__)
int scan() { return getchar(); }
void scan(int &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> &);
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...);
}

template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }
template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }
vi iota(int n) {
    vi a(n);
    iota(all(a), 0);
    return a;
}
template <typename T> vi iota(vector<T> &a, bool greater = false) {
    vi res(a.size());
    iota(all(res), 0);
    sort(all(res), [&](int i, int j) {
        if(greater) return a[i] > a[j];
        return a[i] < a[j];
    });
    return res;
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())

template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}

template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x + y - 1) / y);
}
template <class T> T POW(T x, int n) {
    T res = 1;
    for(; n; n >>= 1, x *= x)
        if(n & 1) res *= x;
    return res;
}
template <class T> T POW(T x, ll n, const ll &mod) {
    T res = 1;
    for(; n; n >>= 1, x = x * x % mod)
        if(n & 1) res = res * x % mod;
    return res;
}
vector<pll> factor(ll x) {
    vector<pll> ans;
    for(ll i = 2; i * i <= x; i++)
        if(x % i == 0) {
            ans.push_back({i, 1});
            while((x /= i) % i == 0) ans.back().second++;
        }
    if(x != 1) ans.push_back({x, 1});
    return ans;
}
template <class T> vector<T> divisor(T x) {
    vector<T> ans;
    for(T i = 1; i * i <= x; i++)
        if(x % i == 0) {
            ans.pb(i);
            if(i * i != x) ans.pb(x / i);
        }
    return ans;
}
template <typename T> void zip(vector<T> &x) {
    vector<T> y = x;
    UNIQUE(y);
    for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
template <class S> void fold_in(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void fold_in(vector<S> &v, Head &&a, Tail &&...tail) {
    for(auto e : a) v.emplace_back(e);
    fold_in(v, tail...);
}
template <class S> void renumber(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void renumber(vector<S> &v, Head &&a, Tail &&...tail) {
    for(auto &&e : a) e = lb(v, e);
    renumber(v, tail...);
}
template <class S, class... Args> vector<S> zip(vector<S> &head, Args &&...args) {
    vector<S> v;
    fold_in(v, head, args...);
    sort(all(v)), v.erase(unique(all(v)), v.end());
    renumber(v, head, args...);
    return v;
}

// x in [l, r)
template <class T, class S> bool inc(const T &x, const S &l, const S &r) { return l <= x and x < r; }
// (a, b) in [lx, rx) * [ly, ry)
template <class T, class S> bool inc(const pair<T, T> &x, const S &lx, const S &ly, const S &rx, const S &ry) { return inc(x.fi, lx, rx) && inc(x.se, ly, ry); }

constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
// bit 演算系
ll pow2(int i) { return 1LL << i; }
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); }
// int allbit(int n) { return (1 << n) - 1; }
ll allbit(ll n) { return (1LL << n) - 1; }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }

ll rnd(ll l, ll r) { //[l, r]
#ifdef _LOCAL
    static mt19937_64 gen;
#else
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

template <class t> void random_shuffle(vc<t> &a) { rep(i, si(a)) swap(a[i], a[rnd(0, i)]); }

int in() {
    int x;
    cin >> x;
    return x;
}
ll lin() {
    unsigned long long x;
    cin >> x;
    return x;
}

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> ll operator*(const pair<T, T> &x, const pair<T, T> &y) { return (ll)x.fi * y.fi + (ll)x.se * y.se; }

template <typename T> struct edge {
    int from, to;
    T cost;
    int id;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
    constexpr bool operator<(const edge<T> &rhs) const noexcept { return cost < rhs.cost; }
    edge &operator=(const int &x) {
        to = x;
        return *this;
    }
    operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;

using Tree = vector<vector<int>>;
using Graph = vector<vector<int>>;
template <class T> using Wgraph = vector<vector<edge<T>>>;
Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {
    Tree res(n);
    if(m == -1) m = n - 1;
    while(m--) {
        int a, b;
        cin >> a >> b;
        a -= margin, b -= margin;
        res[a].emplace_back(b);
        if(!directed) res[b].emplace_back(a);
    }
    return res;
}
template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {
    Wgraph<T> res(n);
    if(m == -1) m = n - 1;
    while(m--) {
        int a, b;
        T c;
        cin >> a >> b >> c;
        a -= margin, b -= margin;
        res[a].emplace_back(b, c);
        if(!directed) res[b].emplace_back(a, c);
    }
    return res;
}
void add(Graph &G, int x, int y) { G[x].eb(y), G[y].eb(x); }
template <class S> void add(Wgraph<S> &G, int x, int y, S c) { G[x].eb(y, c), G[y].eb(x, c); }

#define i128 __int128_t
#define ull unsigned long long int
#define TEST                                                                                                                                                   \
    INT(testcases);                                                                                                                                            \
    while(testcases--)
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
    for(auto it = begin(v); it != end(v); ++it) {
        if(it == begin(v))
            os << *it;
        else
            os << " " << *it;
    }
    return os;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <class S, class T> string to_string(pair<S, T> p) { return "(" + to_string(p.first) + "," + to_string(p.second) + ")"; }
string to_string(string s) { return "\"" + s + "\""; }
string to_string(char c) { return string(1, c); }
template <class T> string to_string(vector<T> s) {
    string res = "{";
    for(auto it = s.begin(); it != s.end(); it++) res += to_string(*it) + (next(it) == s.end() ? "" : ", ");
    return res + "}";
}
template <class T> string to_string(set<T> s) {
    string res = "{";
    for(auto it = s.begin(); it != s.end(); it++) res += to_string(*it), res += (next(it) == end(s) ? "" : ", ");
    return res + "}";
}

#define endl '\n'

#ifdef _LOCAL
void dump() { cerr << endl; }
template <class Head, class... Tail> void dump(Head head, Tail... tail) {
    cerr << to_string(head) << " ";
    dump(tail...);
}
#undef endl
#define debug(x)                                                                                                                                               \
    cout << #x << ": ";                                                                                                                                        \
    dump(x)
#else
void dump() {}
template <class Head, class... Tail> void dump(Head head, Tail... tail) {}
#define debug(x)
#endif
template <class T> void print(const T &a) { cout << a; }
void OUT() { cout << endl; }
template <class Head, class... Tail> void OUT(const Head &head, const Tail &...tail) {
    print(head);
    if(sizeof...(tail)) cout << ' ';
    OUT(tail...);
}

template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(15);
    }
} setup_io;
#define drop(s) cout << #s << endl, exit(0)

template <int N> struct ndFORarray {
    std::array<int, N> v;
    ndFORarray(std::array<int, N> v_) : v(v_) {}
    struct ndFORitr {
        const std::array<int, N> &v;
        std::array<int, N> tmp;
        bool is_end;
        ndFORitr(const std::array<int, N> &v_) : v(v_), tmp(), is_end(false) {}
        bool operator!=(const ndFORitr &) const { return !is_end; }
        void operator++() {
            int pos = N - 1;
            while(pos != -1) {
                tmp[pos] += 1;
                if(tmp[pos] == v[pos]) {
                    tmp[pos] = 0;
                    pos -= 1;
                } else {
                    break;
                }
            }
            if(pos == -1) { is_end = true; }
        }
        const std::array<int, N> &operator*() const { return tmp; }
    };
    ndFORitr begin() const { return ndFORitr(v); }
    ndFORitr end() const { return ndFORitr(v); }
};

struct ndFORvector {
    std::vector<int> v;
    ndFORvector(std::vector<int> v_) : v(v_) {}
    struct ndFORitr {
        const std::vector<int> &v;
        std::vector<int> tmp;
        bool is_end;
        ndFORitr(const std::vector<int> &v_) : v(v_), tmp(v.size(), 0), is_end(false) {}
        bool operator!=(const ndFORitr &) const { return !is_end; }
        void operator++() {
            int pos = v.size() - 1;
            while(pos != -1) {
                tmp[pos] += 1;
                if(tmp[pos] == v[pos]) {
                    tmp[pos] = 0;
                    pos -= 1;
                } else {
                    break;
                }
            }
            if(pos == -1) { is_end = true; }
        }
        const std::vector<int> &operator*() const { return tmp; }
    };
    ndFORitr begin() const { return ndFORitr(v); }
    ndFORitr end() const { return ndFORitr(v); }
};

auto ndFOR(std::vector<int> v) { return ndFORvector(v); }
template <class... Ts> auto ndFOR(Ts... v) { return ndFORarray<std::tuple_size<std::tuple<Ts...>>::value>({v...}); }
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(std::forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, std::forward<Args>(args)...); }
};

template <class S> vector<pair<S, int>> runLength(const vector<S> &v) {
    vector<pair<S, int>> res;
    for(auto &e : v) {
        if(res.empty() or res.back().fi != e)
            res.eb(e, 1);
        else
            res.back().se++;
    }
    return res;
}
vector<pair<char, int>> runLength(const string &v) {
    vector<pair<char, int>> res;
    for(auto &e : v) {
        if(res.empty() or res.back().fi != e)
            res.eb(e, 1);
        else
            res.back().se++;
    }
    return res;
}

template <class T, class F> T bin_search(T ok, T ng, const F &f) {
    while(abs(ok - ng) > 1) {
        T mid = ok + ng >> 1;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
#pragma endregion

// https://judge.yosupo.jp/submission/23126
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;
}

uint64_t gcd_impl(uint64_t n, uint64_t m) {
    constexpr uint64_t K = 5;
    for(int i = 0; i < 80; ++i) {
        uint64_t t = n - m;
        uint64_t s = n - m * K;
        bool q = t < m;
        bool p = t < m * K;
        n = q ? m : t;
        m = q ? t : m;
        if(m == 0) return n;
        n = p ? n : s;
    }
    return gcd_impl(m, n % m);
}

uint64_t gcd_pre(uint64_t n, uint64_t m) {
    for(int i = 0; i < 4; ++i) {
        uint64_t t = n - m;
        bool q = t < m;
        n = q ? m : t;
        m = q ? t : m;
        if(m == 0) return n;
    }
    return gcd_impl(n, m);
}

uint64_t gcd_fast(uint64_t n, uint64_t m) { return n > m ? gcd_pre(n, m) : gcd_pre(m, n); }

template <typename T = int32_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 = int32_t, typename U = int64_t> T modpow(T a, U n, T p) {
    T ret = 1;
    for(; n; n >>= 1, a = U(a) * a % p)
        if(n & 1) ret = U(ret) * a % p;
    return ret;
}

} // namespace inner

using namespace std;

unsigned long long rng() {
    static unsigned long long x_ = 88172645463325252ULL;
    x_ = x_ ^ (x_ << 7);
    return x_ = x_ ^ (x_ >> 9);
}
using namespace std;

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;

using namespace std;

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_fast(q.get(), n);
            }
        }
        if(g == n) do
                g = inner::gcd_fast((x - (ys = f(ys))).get(), n);
            while(g == 1);
        if(g != n) return g;
    }
    exit(1);
}

vector<u64> inner_factorize(u64 n) {
    if(n <= 1) return {};
    u64 p;
    if(n <= (1LL << 30))
        p = pollard_rho<ArbitraryLazyMontgomeryModInt>(n);
    else
        p = pollard_rho<montgomery64>(n);
    if(p == n) return {p};
    auto l = inner_factorize(p);
    auto r = inner_factorize(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}

vector<u64> factorize(u64 n) {
    auto ret = inner_factorize(n);
    sort(begin(ret), end(ret));
    return ret;
}

} // namespace fast_factorize
using fast_factorize::factorize;
using fast_factorize::is_prime;
int main() {
    LL(l, r);
    // (a + b) * (b - a + 1) / 2
    ll ans = 0;
    rep2(i, l, r - 1) {
        if(is_prime(i * 2 + 1)) ans++;
    }
    rep2(i, l, r) if(is_prime(i)) ans++;
    OUT(ans);
}