結果
| 問題 |
No.916 Encounter On A Tree
|
| ユーザー |
 バイト
|
| 提出日時 | 2019-10-25 23:33:58 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 433 ms / 2,000 ms |
| コード長 | 48,017 bytes |
| コンパイル時間 | 3,355 ms |
| コンパイル使用メモリ | 232,052 KB |
| 実行使用メモリ | 323,928 KB |
| 最終ジャッジ日時 | 2024-09-13 09:14:33 |
| 合計ジャッジ時間 | 19,487 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 56 |
ソースコード
//#pragma GCC optimize ("-O3")
#include <bits/stdc++.h>
using namespace std;
//@起動時
struct initon {
initon() {
cin.tie(0);
ios::sync_with_stdio(false);
cout.setf(ios::fixed);
cout.precision(16);
srand((unsigned) clock() + (unsigned) time(NULL));
};
} __initon;
//衝突対策
#define ws ___ws
struct T {
int f, s, t;
T() { f = -1, s = -1, t = -1; }
T(int f, int s, int t) : f(f), s(s), t(t) {}
bool operator<(const T &r) const {
return f != r.f ? f < r.f : s != r.s ? s < r.s : t < r.t;
//return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 大きい順
}
bool operator>(const T &r) const {
return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t;
//return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 小さい順
}
bool operator==(const T &r) const {
return f == r.f && s == r.s && t == r.t;
}
bool operator!=(const T &r) const {
return f != r.f || s != r.s || t != r.t;
}
int operator[](int i) {
assert(i < 3);
return i == 0 ? f : i == 1 ? s : t;
}
};
#define int long long
#define ll long long
#define double long double
#define pow powl
#define ull unsigned long long
using dou = double;
using itn = int;
using str = string;
using bo= bool;
#define au auto
using P = pair<ll, ll>;
#define fi first
#define se second
#define vec vector
#define beg begin
#define rbeg rbegin
#define con continue
#define bre break
#define brk break
#define is ==
//マクロ省略系 コンテナ
//マクロ省略系 コンテナ
using vi = vector<ll>;
using vb = vector<bool>;
using vs = vector<string>;
using vd = vector<double>;
using vc = vector<char>;
using vp = vector<P>;
using vt = vector<T>;
#define vec vector
#define o_vvt(o1, o2, o3, o4, name, ...) name
#define vvt0(t) vec<vec<t>>
#define vvt1(t, a) vec<vec<t>>a
#define vvt2(t, a, b) vec<vec<t>>a(b)
#define vvt3(t, a, b, c) vec<vec<t>> a(b,vec<t>(c))
#define vvt4(t, a, b, c, d) vec<vec<t>> a(b,vec<t>(c,d))
#define vvi(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(ll,__VA_ARGS__)
#define vvb(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(bool,__VA_ARGS__)
#define vvs(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(string,__VA_ARGS__)
#define vvd(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(double,__VA_ARGS__)
#define vvc(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(char,__VA_ARGS__)
#define vvp(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(P,__VA_ARGS__)
#define vvt(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(T,__VA_ARGS__)
template<typename T> vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T, typename... Ts> auto make_v(size_t a, Ts... ts) { return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...)); }
#define vni(name, ...) auto name = make_v<ll>(__VA_ARGS__)
#define vnb(name, ...) auto name = make_v<bool>(__VA_ARGS__)
#define vns(name, ...) auto name = make_v<string>(__VA_ARGS__)
#define vnd(name, ...) auto name = make_v<double>(__VA_ARGS__)
#define vnc(name, ...) auto name = make_v<char>(__VA_ARGS__)
#define vnp(name, ...) auto name = make_v<P>(__VA_ARGS__)
#define v3i(a, b, c, d) vector<vector<vi>> a(b, vector<vi>(c, vi(d)))
#define v3d(a, b, c, d) vector<vector<vd>> a(b, vector<vd>(c, vd(d)))
#define v3m(a, b, c, d) vector<vector<vm>> a(b, vector<vm>(c, vm(d)))
#define _vvi vector<vi>
#define _vvl vector<vl>
#define _vvb vector<vb>
#define _vvs vector<vs>
#define _vvd vector<vd>
#define _vvc vector<vc>
#define _vvp vector<vp>
#define PQ priority_queue<ll, vector<ll>, greater<ll> >
#define tos to_string
using mapi = map<int, int>;
using mapd = map<dou, int>;
using mapc = map<char, int>;
using maps = map<str, int>;
using seti = set<int>;
using setd = set<dou>;
using setc = set<char>;
using sets = set<str>;
using qui = queue<int>;
#define bset bitset
#define uset unordered_set
#define mset multiset
#define umap unordered_map
#define umapi unordered_map<int,int>
#define umapp unordered_map<P,int>
#define mmap multimap
//マクロ 繰り返し
#define _overloadrep(_1, _2, _3, _4, name, ...) name
# define _rep(i, n) for(int i = 0,_lim=n; i < _lim ; i++)
#define repi(i, m, n) for(int i = m,_lim=n; i < _lim ; i++)
#define repadd(i, m, n, ad) for(int i = m,_lim=n; i < _lim ; i+= ad)
#define rep(...) _overloadrep(__VA_ARGS__,repadd,repi,_rep,)(__VA_ARGS__)
#define _rer(i, n) for(int i = n; i >= 0 ; i--)
#define reri(i, m, n) for(int i = m,_lim=n; i >= _lim ; i--)
#define rerdec(i, m, n, dec) for(int i = m,_lim=n; i >= _lim ; i-=dec)
#define rer(...) _overloadrep(__VA_ARGS__,rerdec,reri,_rer,)(__VA_ARGS__)
#define fora(a, b) for(auto&& a : b)
//マクロ 定数
#define k3 1010
#define k4 10101
#define k5 101010
#define k6 1010101
#define k7 10101010
const int inf = (int) 1e9 + 100;
const ll linf = (ll) 1e18 + 100;
const double eps = 1e-9;
const double PI = 3.1415926535897932384626433832795029L;
ll ma = numeric_limits<ll>::min();
ll mi = numeric_limits<ll>::max();
const int y4[] = {-1, 1, 0, 0};
const int x4[] = {0, 0, -1, 1};
const int y8[] = {0, 1, 0, -1, -1, 1, 1, -1};
const int x8[] = {1, 0, -1, 0, 1, -1, 1, -1};
//マクロ省略形 関数等
#define arsz(a) (sizeof(a)/sizeof(a[0]))
#define sz(a) ((int)(a).size())
#define rs resize
#define mp make_pair
#define pb push_back
#define pf push_front
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
inline void sort(string &a) { sort(a.begin(), a.end()); }
template<class T> inline void sort(vector<T> &a) { sort(a.begin(), a.end()); };
template<class T> inline void sort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len); };
template<class T, class F> inline void sort(vector<T> &a, F f) { sort(a.begin(), a.end(), [&](T l, T r) { return f(l) < f(r); }); };
enum ___pcomparator {
fisi, fisd, fdsi, fdsd, sifi, sifd, sdfi, sdfd
};
inline void sort(vector<P> &a, ___pcomparator type) {
switch (type) {
case fisi:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se < r.se; });
break;
case fisd:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi < r.fi : l.se > r.se; });
break;
case fdsi:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se < r.se; });
break;
case fdsd:
sort(all(a), [&](P l, P r) { return l.fi != r.fi ? l.fi > r.fi : l.se > r.se; });
break;
case sifi:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi < r.fi; });
break;
case sifd:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se < r.se : l.fi > r.fi; });
break;
case sdfi:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi < r.fi; });
break;
case sdfd:
sort(all(a), [&](P l, P r) { return l.se != r.se ? l.se > r.se : l.fi > r.fi; });
break;
}
};
inline void sort(vector<T> &a, ___pcomparator type) {
switch (type) {
case fisi:
sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f < r.f : l.s < r.s; });
break;
case
fisd:
sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f < r.f : l.s > r.s; });
break;
case
fdsi:
sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f > r.f : l.s < r.s; });
break;
case
fdsd:
sort(all(a), [&](T l, T r) { return l.f != r.f ? l.f > r.f : l.s > r.s; });
break;
case
sifi:
sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s < r.s : l.f < r.f; });
break;
case
sifd:
sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s < r.s : l.f > r.f; });
break;
case
sdfi:
sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s > r.s : l.f < r.f; });
break;
case
sdfd:
sort(all(a), [&](T l, T r) { return l.s != r.s ? l.s > r.s : l.f > r.f; });
break;
}
};
template<class T> inline void rsort(vector<T> &a) { sort(a.begin(), a.end(), greater<T>()); };
template<class T> inline void rsort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len, greater<T>()); };
template<class U, class F> inline void rsort(vector<U> &a, F f) { sort(a.begin(), a.end(), [&](U l, U r) { return f(l) > f(r); }); };
template<class U> inline void sortp(vector<U> &a, vector<U> &b) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
sort(c);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;;
}
};
//F = T<T>
//例えばreturn p.fi + p.se;
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, F f) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
sort(c, f);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, char type) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
sort(c, type);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U> inline void rsortp(vector<U> &a, vector<U> &b) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
rsort(c);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U, class F> inline void rsortp(vector<U> &a, vector<U> &b, F f) {
vp c;
int n = sz(a);
assert(n == sz(b));
rep(i, n)c.eb(a[i], b[i]);
rsort(c, f);
rep(i, n) {
a[i] = c[i].first;
b[i] = c[i].second;
}
};
template<class U> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c) {
vt r;
int n = sz(a);
assert(n == sz(b));
assert(n == sz(c));
rep(i, n)r.eb(a[i], b[i], c[i]);
sort(r);
rep(i, n) {
a[i] = r[i].f;
b[i] = r[i].s;
c[i] = r[i].t;
}
};
template<class U, class F> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
vt r;
int n = sz(a);
assert(n == sz(b));
assert(n == sz(c));
rep(i, n)r.eb(a[i], b[i], c[i]);
sort(r, f);
rep(i, n) {
a[i] = r[i].f;
b[i] = r[i].s;
c[i] = r[i].t;
}
};
template<class U, class F> inline void rsortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
vt r;
int n = sz(a);
assert(n == sz(b));
assert(n == sz(c));
rep(i, n)r.eb(a[i], b[i], c[i]);
rsort(r, f);
rep(i, n) {
a[i] = r[i].f;
b[i] = r[i].s;
c[i] = r[i].t;
}
};
template<class T> inline void sort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)sort(a[i]); }
template<class T> inline void rsort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)rsort(a[i]); }
template<typename A, size_t N, typename T> void fill(A (&a)[N], const T &v) { rep(i, N)a[i] = v; }
template<typename A, size_t N, size_t O, typename T> void fill(A (&a)[N][O], const T &v) { rep(i, N)rep(j, O)a[i][j] = v; }
template<typename A, size_t N, size_t O, size_t P, typename T> void fill(A (&a)[N][O][P], const T &v) { rep(i, N)rep(j, O)rep(k, P)a[i][j][k] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, typename T> void fill(A (&a)[N][O][P][Q], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)a[i][j][k][l] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, typename T> void fill(A (&a)[N][O][P][Q][R], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)a[i][j][k][l][m] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S, typename T> void fill(A (&a)[N][O][P][Q][R][S], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)a[i][j][k][l][m][n] = v; }
template<typename V, typename T>
void fill(V &xx, const T vall) {
xx = vall;
}
template<typename V, typename T>
void fill(vector<V> &vecc, const T vall) {
for (auto &&vx: vecc) fill(vx, vall);
}
//@汎用便利関数 入力
template<typename T = int> T _in() {
T x;
cin >> x;
return (x);
}
#define _overloadin(_1, _2, _3, _4, name, ...) name
#define in0() _in()
#define in1(a) cin>>a
#define in2(a, b) cin>>a>>b
#define in3(a, b, c) cin>>a>>b>>c
#define in4(a, b, c, d) cin>>a>>b>>c>>d
#define in(...) _overloadin(__VA_ARGS__,in4,in3,in2 ,in1,in0)(__VA_ARGS__)
#define _overloaddin(_1, _2, _3, _4, name, ...) name
#define din1(a) int a;cin>>a
#define din2(a, b) int a,b;cin>>a>>b
#define din3(a, b, c) int a,b,c;cin>>a>>b>>c
#define din4(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d
#define din(...) _overloadin(__VA_ARGS__,din4,din3,din2 ,din1)(__VA_ARGS__)
#define _overloaddind(_1, _2, _3, _4, name, ...) name
#define din1d(a) int a;cin>>a;a--
#define din2d(a, b) int a,b;cin>>a>>b;a--,b--
#define din3d(a, b, c) int a,b,c;cin>>a>>b>>c;a--,b--,c--
#define din4d(a, b, c, d) int a,b,c,d;cin>>a>>b>>c>>d;;a--,b--,c--,d--
#define dind(...) _overloaddind(__VA_ARGS__,din4d,din3d,din2d ,din1d)(__VA_ARGS__)
string sin() { return _in<string>(); }
ll lin() { return _in<ll>(); }
#define na(a, n) a.resize(n); rep(nai,n) cin >> a[nai];
#define nao(a, n) a.resize(n+1); rep(i,n) cin >> a[i+1];
#define nad(a, n) a.resize(n); rep(i,n){ cin >> a[i]; a[i]--;}
#define na2(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i];
#define na2d(a, b, n) a.resize(n),b.resize(n);rep(i, n){cin >> a[i] >> b[i];a[i]--,b[i]--;}
#define na3(a, b, c, n) a.resize(n),b.resize(n),c.resize(n); rep(i, n)cin >> a[i] >> b[i] >> c[i];
#define na3d(a, b, c, n) a.resize(n),b.resize(n),c.resize(n); rep(i, n){cin >> a[i] >> b[i] >> c[i];a[i]--,b[i]--,c[i]--;}
#define nt(a, h, w) a.resize(h);rep(i,h)a[i].resize(w); rep(hi,h)rep(wi,w) cin >> a[hi][wi];
#define ntd(a, h, w) rs(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi], a[hi][wi]--;
#define ntp(a, h, w) fill(a,'#');rep(hi,1,h+1)rep(wi,1,w+1) cin >> a[hi][wi];
#ifdef _DEBUG
template<class T> void err2(T &&head) { cerr << head; }
template<class T, class... U> void err2(T &&head, U &&... tail) {
cerr << head << " ";
err2(tail...);
}
template<class T, class... U> void err(T &&head, U &&... tail) {
cerr << head << " ";
err2(tail...);
cerr << "" << endl;
}
template<class T> void err(T &&head) { cerr << head << endl; }
void err() { cerr << "" << endl; }
template<class T> string out_m2(vector<T> &a, ll W = inf) {
stringstream ss;
if (W == inf)W = min(sz(a), 12ll);
if (sz(a) == 0)return ss.str();
rep(i, W) { ss << a[i] << " "; }
return ss.str();
}
template<class T> string out_m2(vector<vector<T> > &a, ll H = inf, ll W = inf, int key = -1) {
H = min({H, sz(a), 12ll});
W = min({W, sz(a[0]), 12ll});
stringstream ss;
ss << endl;
if (key == -1)ss << " *|"; else ss << " " << key << "|";
rep(w, W)ss << std::right << std::setw(4) << w;
ss << "" << endl;
rep(w, W * 4 + 3)ss << "_";
ss << "" << endl;
rep(h, H) {
ss << std::right << std::setw(2) << h << "|";
rep(w, min(sz(a[h]), 12ll)) { if (abs(a[h][w]) == linf) ss << " e" << ""; else ss << std::right << std::setw(4) << a[h][w]; }
ss << "" << endl;
}
return ss.str();
}
/*@formatter:off*/
template<class T> string out_m2(vector<vector<vector<T> > > &a, ll H = inf, ll W = inf, ll U = inf) {stringstream ss; if (H == inf)H = 5; H = min(H, sz(a)); rep(i, H) { ss << endl; ss << out_m2(a[i], W, U, i); } return ss.str();}
string out_m2(int a) {stringstream ss;ss << a;return ss.str();}
template<class T> string out_m2(T &a) {stringstream ss;ss << a;return ss.str();}
template<class T> string out_m(vector<T> &a, ll W = inf) {stringstream ss; if (W == inf)W = min(sz(a), 12ll); if(sz(a)==0)return ss.str(); rep(i, W) { ss << a[i] << " "; } ss << "" << endl; return ss.str();}
template<class T> string out_m(vector<vector<T> > &a, ll H = inf, ll W = inf, int key = -1) {
H = min({H, sz(a), 12ll});
W = min({W, sz(a[0]), 12ll});
stringstream ss;
ss << endl;
if (key == -1)ss << " *|"; else ss << " " << key << "|";
rep(w, W)ss << std::right << std::setw(4) << w;
ss << "" << endl;
rep(w, W * 4 + 3)ss << "_";
ss << "" << endl;
rep(h, H) {
ss << std::right << std::setw(2) << h << "|";
rep(w, min(sz(a[h]),12ll)) { if (abs(a[h][w]) == linf) ss << " e" << ""; else ss << std::right << std::setw(4) << a[h][w]; }
ss << "" << endl;
}
ss << endl;
return ss.str();
}
/*@formatter:off*/
template<class T> string out_m(vector<vector<vector<T> > > &a, ll H = inf, ll W = inf, ll U = inf) {stringstream ss; if (H == inf)H = 5; H = min(H, sz(a)); rep(i, H) { ss << endl; ss << out_m(a[i], W, U, i); } ss << endl; return ss.str();}
string out_m(int a) {stringstream ss;ss << a << endl;return ss.str();}
template<class T> string out_m(T &a) {stringstream ss;ss << a << endl;return ss.str();}
template<class T> void outv(vector<T> &a, ll W=inf) {cout << out_m(a,W) << endl;}
template<class T> void outv(vector<vector<T> > &a, ll H = linf, ll W = linf,int key=-1) { cout << out_m(a,H,W,key) << endl;}
template<class T> void outv(vector<vector<vector<T> > > &a, ll H = linf, ll W = linf,ll U = linf) {cout << out_m(a,H,W,U)<< endl;}
#else
template<class T> void outv(vector<T> &a, ll W = inf) {
rep(i, min(W, sz(a))) { cout << a[i] << " "; }
cout << "" << endl;
}
template<class T> void outv(vector<vector<T> > &a, ll H = linf, ll W = linf, int key = -1) { rep(i, min(H, sz(a))) { outv(a[i], W); }}
template<class T> void outv(vector<vector<vector<T> > > &a, ll H = linf, ll W = linf, ll U = linf) { ; }
#define err(...);
#endif
#define debugName(VariableName) # VariableName
#define deb1(x) debugName(x)<<" = "<<out_m2(x)
#define deb2(x, ...) deb1(x) <<", "<< deb1(__VA_ARGS__)
#define deb3(x, ...) deb1(x) <<", "<< deb2(__VA_ARGS__)
#define deb4(x, ...) deb1(x) <<", "<< deb3(__VA_ARGS__)
#define deb5(x, ...) deb1(x) <<", "<< deb4(__VA_ARGS__)
#define deb6(x, ...) deb1(x) <<", "<< deb5(__VA_ARGS__)
#define deb7(x, ...) deb1(x) <<", "<< deb6(__VA_ARGS__)
#define deb8(x, ...) deb1(x) <<", "<< deb7(__VA_ARGS__)
#define deb9(x, ...) deb1(x) <<", "<< deb8(__VA_ARGS__)
#define deb10(x, ...) deb1(x) <<", "<< deb9(__VA_ARGS__)
#define o_ebug(o1, o2, o3, o4, o5, o6, o7, o8, o9, o10, name, ...) name
#ifdef _DEBUG
#define deb(...) cerr<< o_ebug(__VA_ARGS__,deb10,deb9,deb8,deb7,deb6,deb5,deb4,deb3,deb2,deb1)(__VA_ARGS__) <<endl
#else
#define deb(...) ;
#endif
#define debugline(x) cerr << x << " " << "(L:" << __LINE__ << ")" << '\n'
void ole() {
#ifdef _DEBUG
debugline("ole");
exit(0);
#endif
string a = "a";
rep(i, 30)a += a;
rep(i, 1 << 17)cout << a << endl;
cout << "OLE 出力長制限超過" << endl;
exit(0);
}
void tle() { while (inf)cout << inf << endl; }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll gcd(vi b) {
ll res = b[0];
for (auto &&v :b)res = gcd(v, res);
return res;
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll rev(ll a) {
ll res = 0;
while (a) {
res *= 10;
res += a % 10;
a /= 10;
}
return res;
}
template<class T> void rev(vector<T> &a) {
reverse(all(a));
}
void rev(string &a) {
reverse(all(a));
}
ll ceil(ll a, ll b) {
if (b == 0) {
debugline("ceil");
deb(a, b);
ole();
return -1;
} else return (a + b - 1) / b;
}
ll sqrt(ll a) {
if (a < 0) {
debugline("sqrt");
deb(a);
ole();
}
ll res = (ll) std::sqrt(a);
while (res * res < a)res++;
return res;
}
double log(double e, double x) { return log(x) / log(e); }
ll sig(ll t) { return (1 + t) * t / 2; }
ll sig(ll s, ll t) { return (s + t) * (t - s + 1) / 2; }
vi divisors(int v) {
vi res;
double lim = std::sqrt(v);
for (int i = 1; i <= lim; ++i) {
if (v % i == 0) {
res.pb(i);
if (i != v / i)res.pb(v / i);
}
}
return res;
}
vb isPrime;
vi primes;
void setPrime() {
int len = 4010101;
isPrime.resize(4010101);
fill(isPrime, true);
isPrime[0] = isPrime[1] = false;
for (int i = 2; i <= sqrt(len) + 5; ++i) {
if (!isPrime[i])continue;
for (int j = 2; i * j < len; ++j) {
isPrime[i * j] = false;
}
}
rep(i, len)if (isPrime[i])primes.pb(i);
}
vi factorization(int v) {
int tv = v;
vi res;
if (isPrime.size() == 0)setPrime();
for (auto &&p :primes) {
if (v % p == 0)res.push_back(p);
while (v % p == 0) {
v /= p;
}
if (v == 1 || p * p > tv)break;
}
if (v > 1)res.pb(v);
return res;
}
inline bool inside(int h, int w, int H, int W) { return h >= 0 && w >= 0 && h < H && w < W; }
inline bool inside(int v, int l, int r) { return l <= v && v < r; }
#define ins inside
ll u(ll a) { return a < 0 ? 0 : a; }
template<class T> vector<T> u(const vector<T> &a) {
vector<T> ret = a;
fora(v, ret)v = u(v);
return ret;
}
#define MIN(a) numeric_limits<a>::min()
#define MAX(a) numeric_limits<a>::max()
void yn(bool a) {
if (a)cout << "yes" << endl;
else cout << "no" << endl;
}
void Yn(bool a) {
if (a)cout << "Yes" << endl;
else cout << "No" << endl;
}
void YN(bool a) {
if (a)cout << "YES" << endl;
else cout << "NO" << endl;
}
void fyn(bool a) {
if (a)cout << "yes" << endl;
else cout << "no" << endl;
exit(0);
}
void fYn(bool a) {
if (a)cout << "Yes" << endl;
else cout << "No" << endl;
exit(0);
}
void fYN(bool a) {
if (a)cout << "YES" << endl;
else cout << "NO" << endl;
exit(0);
}
void Possible(bool a) {
if (a)cout << "Possible" << endl;
else cout << "Impossible" << endl;
exit(0);
}
void POSSIBLE(bool a) {
if (a)cout << "POSSIBLE" << endl;
else cout << "IMPOSSIBLE" << endl;
exit(0);
}
template<class T, class U> set<T> &operator+=(set<T> &a, U v) {
a.insert(v);
return a;
}
template<class T, class U> vector<T> &operator+=(vector<T> &a, U v) {
a.pb(v);
return a;
}
template<class T> T sum(vector<T> &v, int s = 0, int t = inf) {
T ret = 0;
rep(i, s, min(sz(v), t))ret += v[i];
return ret;
}
void mod(int &a, int m) { a = (a % m + m) % m; }
template<class F> inline int mgr(int ok, int ng, F f) {
#define _mgrbody int mid = (ok + ng) / 2; if (f(mid))ok = mid; else ng = mid;
if (ok < ng)while (ng - ok > 1) { _mgrbody } else while (ok - ng > 1) { _mgrbody }
return ok;
}
template<class F> inline int mgr(int ok, int ng, int second, F f) {
#define _mgrbody2 int mid = (ok + ng) / 2; if (f(mid, second))ok = mid; else ng = mid;
if (ok < ng) while (ng - ok > 1) { _mgrbody2 } else while (ok - ng > 1) { _mgrbody2 }
return ok;
}
template<typename T> ostream &operator<<(ostream &os, vector<T> &m) {
for (auto &&v:m) os << v << " ";
return os;
}
constexpr bool bget(ll m, int keta) { return (m >> keta) & 1; }
int bget(ll m, int keta, int sinsuu) {
m /= (ll) pow(sinsuu, keta);
return m % sinsuu;
}
ll bit(int n) { return (1LL << (n)); }
ll bit(int n, int sinsuu) { return (ll) pow(sinsuu, n); }
int mask(int n) { return (1ll << n) - 1; }
#define bcou __builtin_popcountll
template<class T> vector<T> ruiv(vector<T> &a) {
vector<T> ret(a.size() + 1);
rep(i, a.size())ret[i + 1] = ret[i] + a[i];
return ret;
}
template<class T, class U> inline bool chma(T &a, const U &b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template<class U> inline bool chma(const U &b) { return chma(ma, b); }
template<class T, class U> inline bool chmi(T &a, const U &b) {
if (b < a) {
a = b;
return true;
}
return false;
}
template<class U> inline bool chmi(const U &b) { return chmi(mi, b); }
#define unique(v) v.erase( unique(v.begin(), v.end()), v.end() );
int max(vi &a) {
int res = a[0];
fora(v, a) {
res = max(res, v);
}
return res;
}
int min(vi &a) {
int res = a[0];
fora(v, a) {
res = min(res, v);
}
return res;
}
template<typename T> class fixed_point : T {public: explicit constexpr fixed_point(T &&t) noexcept: T(std::forward<T>(t)) {} template<typename... Args> constexpr decltype(auto) operator()(Args &&... args) const { return T::operator()(*this, std::forward<Args>(args)...); }};template<typename T> static inline constexpr decltype(auto) fix(T &&t) noexcept { return fixed_point<T>{std::forward<T>(t)}; }
/*@formatter:on*/
int N, K, H, W;
vi A, B, C;
//@formatter:off
//よく使うクラス、構造体
struct unionfind {
vector<ll> par;
vector<ll> siz;
vector<ll> es;
ll n, trees;//連結グループの数(親の種類)
unionfind(ll n) : n(n), trees(n) { par.resize(n); siz.resize(n); es.resize(n); for (ll i = 0; i < n; i++) { par[i] = i; siz[i] = 1; } }
ll root(ll x) { if (par[x] == x) { return x; } else { return par[x] = root(par[x]); }}
bool unite(ll x, ll y) {
x = root(x);
y = root(y);
es[x]++;
if (x == y) return false;
if (siz[x] > siz[y]) swap(x, y);
trees--;
par[x] = y;
siz[y] += siz[x];
es[y] += es[x];
return true;
}
bool same(ll x, ll y) { return root(x) == root(y); }
ll size(ll x) { return siz[root(x)]; }
ll esize(ll x) { return es[root(x)]; }
vi sizes(){ vi cou(n); vi ret; ret.reserve(n); rep(i, n){ cou[root (i)]++; } rep(i, n){ if(cou[i])ret.push_back(cou[i]); } return ret; }
//つながりを無向グラフと見なし、xが閉路に含まれるか判定
bool close(ll x) { return esize(x) >= size(x); }
vec<vi> sets() { vi ind(n, -1); ll i = 0; vvi(res, trees); rep(j, n) { ll r = root(j); if (ind[r] == -1)ind[r] = i++; res[ind[r]].push_back(j); } rep(i, trees) { ll r = root(res[i][0]); if (res[i][0] == r)continue; rep(j, 1, sz(res[i])) { if (res[i][j] == r) { swap(res[i][0], res[i][j]); break; } } } return res; }
};
/*@formatter:off*/
#define forg(gi, ve) for (ll gi = 0,forglim = ve.size(), f, t, c; gi < forglim && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, true); ++gi)
#define fort(gi, ve) for (ll gi = 0, f, t, c; gi < ve.size() && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, true); ++gi)if(t!=p)
#define fore(gi, ve) for (ll gi = 0,forglim = ve.size(), f, t, c,ty, id; gi < forglim && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c, id=ve[gi].id, ty = ve[gi].ty, true); ++gi)
//typeが追加される
#define forg2(gi, ve) for (ll gi = 0,forglim = ve.size(), f, t, c,ty; gi < forglim && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c,ty=ve[gi].ty, true); ++gi)
#define fort2(gi, ve) for (ll gi = 0, f, t, c,ty; gi < ve.size() && (f = ve[gi].f, t = ve[gi].t, c = ve[gi].c,ty=ve[gi].ty, true); ++gi)if(t!=p)
template<class T> struct edge { int f, t; T c; int id; int ty; edge(int f, int t, T c = 1, int ty = -1,int id = -1) : f(f), t(t), c(c), id(id), ty(ty) {} bool operator<(const edge &b) const { return c < b.c; } bool operator>(const edge &b) const { return c > b.c; }};
template<class T> ostream &operator<<(ostream &os, edge<T> &e) { os << e.f << " " << e.t << " " << e.c; return os;}
template<typename T> class graph {protected: vector<bool> usedv;public : vector<vector<edge<T>>> g; vector<edge<T>> edges; int n; graph(int n) : n(n) { g.resize(n), usedv.resize(n); } void clear() { g.clear(), edges.clear(); } void resize(int n) { this->n = n; g.resize(n); usedv.resize(n); } int size() { return g.size(); } vector<edge<T> > &operator[](int i) { return g[i]; } virtual void add(int f, int t, T c, int ty ,int id) = 0; virtual bool used(edge<T> &e) = 0; virtual bool used(int id) = 0; virtual void del(edge<T> &e) = 0; virtual void del(int id) = 0; virtual void set_edges() = 0;};
template<typename T =ll> class digraph : public graph<T> {
public:
using graph<T>::g;
using graph<T>::n;
using graph<T>::edges;
using graph<T>::usedv;
int eid = 0;
digraph(int n) : graph<T>(n) {}
void add(int f, int t, T c = 1, int ty = -1,int id = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n)) {
debugline("digraph add");
deb(f, t, c, ty,id);
ole();
}
if (id == -1)id = eid++;
g[f].emplace_back(f, t, c, ty,id);
edges.emplace_back(f, t, c, ty,id);
}
void ing(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t; cin >> f >> t; f -= minus; t -= minus; add(f, t); } }
void ingc(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t, c; cin >> f >> t >> c; f -= minus; t -= minus; add(f, t,c); } }
void ingct(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t, c,ty; cin >> f >> t >> c>>ty; f -= minus; t -= minus; ty -= minus; add(f, t,c,ty); } }
void ingtc(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t, c,ty; cin >> f >> t >> ty>>c; f -= minus; t -= minus; ty -= minus; add(f, t,c,ty); } }
bool used(edge<T> &e) { return usedv[e.id]; }
bool used(int id) { return usedv[id]; }
void del(edge<T> &e) { usedv[e.id] = 1; }
void del(int id) { usedv[id] = 1; }
void set_edges() { if (sz(edges))return; rep(i, n)fora(e, g[i])edges.push_back(e); }
};
template<class T=int> class undigraph : public graph<T> {
public:
using graph<T>::g; using graph<T>::n; using graph<T>::edges; using graph<T>::usedv;
int eid = 0;
undigraph(int n) : graph<T>(n) {}
// f < t
void add(int f, int t, T c = 1, int ty = -1, int id = -1) {
if (!(0 <= f && f < n && 0 <= t && t < n)) {
debugline("undigraph add");
deb(f, t, c, ty, id);
ole();
}
if (id == -1)id = eid++;
g[f].emplace_back(f, t, c, ty, id);
g[t].emplace_back(t, f, c, ty, id);
edges.emplace_back(f, t, c, ty, id);//
edges.emplace_back(t, f, c, ty, id);
}
void add(edge<T> &e) { int f = e.f, t = e.t, ty = e.ty; T c = e.c; add(f, t, c, ty); }
void ing(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t; cin >> f >> t; f -= minus; t -= minus; add(f, t); } } void ingc(int n, int m, int minus = 1) {rep(i, m) { this->resize(n); int f, t, c; cin >> f >> t >> c; f -= minus; t -= minus; add(f, t, c); }}
void ingct(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t, c, ty; cin >> f >> t >> c >> ty; f -= minus; t -= minus; ty -= minus; add(f, t, c, ty); } }
void ingtc(int n,int m, int minus = 1) { this->resize(n); rep(i, m) { int f, t, c, ty; cin >> f >> t >> ty >> c; f -= minus; t -= minus; ty -= minus; add(f, t, c, ty); } } bool used(edge<T> &e) { return usedv[e.id]; }
bool used(int id) { return usedv[id]; }
void del(edge<T> &e) { usedv[e.id] = 1; }
void del(int id) { usedv[id] = 1; }
void set_edges() { if (sz(edges))return; rep(i, n)fora(e, g[i])edges.push_back(e); }
};
template<class T> class MinOp { public: T operator()(T a, T b) { return min(a, b); }};
template<typename OpFunc> struct SparseTable {
OpFunc op;
signed size;
vector<signed> lg;
vector<vector<pair<signed, signed>>> table;
void init(const vector<pair<signed, signed>> &array, OpFunc opfunc) {
signed n = array.size();
op = opfunc;
lg.assign(n + 1, 0);
for (signed i = 1; i <= n; i++) { lg[i] = 31 - __builtin_clz(i); }
table.assign(lg[n] + 1, array);
for (signed i = 1; i <= lg[n]; i++) { for (signed j = 0; j < n; j++) { if (j + (1 << (i - 1)) < n) { table[i][j] = op(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]); } else { table[i][j] = table[i - 1][j]; }}}
}
pair<signed, signed> query(signed l, signed r) {
assert(l < r);
return op(table[lg[r - l]][l], table[lg[r - l]][r - (1 << lg[r - l])]);
}
};
struct PMORMQ {
vector<signed> a;
SparseTable<MinOp<pair<signed, signed> > > sparse_table;
vector<vector<vector<signed> > > lookup_table;
vector<signed> block_type;
signed block_size, n_block;
void init(const vector<signed> &array) {
a = array;
signed n = a.size();
block_size = std::max(1, (31 - __builtin_clz(n)) / 2);
while (n % block_size != 0) {
a.push_back(a.back() + 1);
n++;
}
n_block = n / block_size;
vector<pair<signed, signed> > b(n_block, make_pair(INT_MAX, INT_MAX));
for (signed i = 0; i < n; i++) { b[i / block_size] = min(b[i / block_size], make_pair(a[i], i)); }
sparse_table.init(b, MinOp<pair<signed, signed> >());
block_type.assign(n_block, 0);
for (signed i = 0; i < n_block; i++) {
signed cur = 0;
for (signed j = 0; j < block_size - 1; j++) {
signed ind = i * block_size + j;
if (a[ind] < a[ind + 1]) { cur |= 1 << j; }
}
block_type[i] = cur;
}
lookup_table.assign(1 << (block_size - 1), vector<vector<signed> >(block_size, vector<signed>(block_size + 1)));
for (signed i = 0; i < (1 << (block_size - 1)); i++) {
for (signed j = 0; j < block_size; j++) {
signed res = 0;
signed cur = 0;
signed pos = j;
for (signed k = j + 1; k <= block_size; k++) {
lookup_table[i][j][k] = pos;
if (i & (1 << (k - 1))) { cur++; } else { cur--; }
if (res > cur) {
pos = k;
res = cur;
}
}
}
}
}
signed query(signed l, signed r) {
assert(l < r);
signed lb = l / block_size;
signed rb = r / block_size;
if (lb == rb) { return lb * block_size + lookup_table[block_type[lb]][l % block_size][r % block_size]; }
signed pl = lb * block_size + lookup_table[block_type[lb]][l % block_size][block_size];
signed pr = rb * block_size + lookup_table[block_type[rb]][0][r % block_size];
signed pos = pl;
if (r % block_size > 0 && a[pl] > a[pr]) { pos = pr; }
if (lb + 1 == rb) { return pos; }
signed spv = sparse_table.query(lb + 1, rb).second;
if (a[pos] > a[spv]) { return spv; }
return pos;
}
};
template<class T=int> class tree : public undigraph<T> {
PMORMQ rmq;
int cnt;
vector<signed> id, in;
bool never = true;
bool never_hld = true;
void dfs(int x, int p, int d, int dis = 0) {
id[cnt] = x;
par[x] = p;
dep.push_back(d);
disv[x] = dis;
in[x] = cnt++;
forg(gi, g[x]) {
if (t == p) { continue; }
dfs(t, x, d + 1, dis + c);
id[cnt] = x;
dep.push_back(d);
cnt++;
}
}
void precalc() {
never = false;
cnt = 0;
dep.clear();
disv.assign(n, 0);
in.assign(n, -1);
id.assign(2 * n - 1, -1);
par.assign(n, -1);
dfs(root, -1, 0);
rmq.init(dep);
#ifdef _DEBUG
if(n>=100)return;
cerr << "---tree---" << endl;
//abcd
rep(i, n) {
if (!(i == root || sz(g[i]) > 1))continue;
cerr << i << " -> ";
vi ts;
forg(gi, g[i]) { if (t != par[i])ts.push_back(t); }
rep(i, sz(ts) - 1)cerr << ts[i] << ", ";
if (sz(ts))cerr << ts.back() << endl;
}
cerr << endl;
#endif
}
int pos;
void hld_build() {
never_hld = false;
if (never)precalc();
pos = 0;
vid.assign(n, -1);
head.assign(n, 0);
sub.assign(n, 1);
hvy.assign(n, -1);
hdep.assign(n, 0);
inv.assign(n, 0);
type.assign(n, 0);
build();
#ifdef _DEBUG
if(n>=100)return;
cerr << "---hld_index---" << endl;
vi inds;
rep(i, n) if (sz(g[i]))inds.push_back(i);
rep(i, sz(inds)) {
str s = tos(bel(inds[i]));
cerr << std::right << std::setw(sz(s) + (i ? 1 : 0)) << inds[i];
}
cerr << endl;
rep(i, sz(inds)) { cerr << bel(inds[i]) << " "; }
cerr << endl << endl;
cerr << "---hld_edge_index---" << endl;
fora(e, edges) { if (e.f <= e.t) cerr << e.f << "-" << e.t << " " << bel(e) << endl; }
cerr << endl << endl;
#endif
}
void build(vector<int> rs = vector<int>(1, 0)) {
int c = 0;
for (int r:rs) {
dfs(r);
bfs(r, c++);
}
}
void dfs(int rt) {
stack<P> st;
hdep[rt] = 0;
st.emplace(rt, 0);
while (!st.empty()) {
int v = st.top().first;
int &i = st.top().second;
if (i < (int) g[v].size()) {
int u = g[v][i++].t;
if (u == par[v]) continue;
hdep[u] = hdep[v] + 1;
st.emplace(u, 0);
} else {
st.pop();
int res = 0;
forg(gi, g[v]) {
int u = t;
if (u == par[v]) continue;
sub[v] += sub[u];
if (res < sub[u]) res = sub[u], hvy[v] = u;
}
}
}
}
void bfs(int r, int c) {
int &k = pos;
queue<int> q({r});
while (!q.empty()) {
int h = q.front();
q.pop();
for (int i = h; i != -1; i = hvy[i]) {
type[i] = c;
vid[i] = k++;
inv[vid[i]] = i;
head[i] = h;
forg(gi, g[i])if (t != par[i] && t != hvy[i]) q.push(t);
}
}
}
vi vid;
public:
using undigraph<T>::g; using undigraph<T>::n; using undigraph<T>::edges; using undigraph<T>::usedv;
vector<int> disv;
vector<signed> dep, par;
vector<int> head, sub, hvy, inv, type, hdep/*おそらくグループ内のdep*/;/*vid := bel()*/ int root;
tree(int n_, int root = 0) : undigraph<T>(n_), root(root) { n = n_; }
int lca(int a, int b) {
if (never)precalc();
int x = in[a];
int y = in[b];
if (x > y) { swap(x, y); }
int pos = rmq.query(x, y + 1);
return id[pos];
}
/*@formatter:on*/
int dis(int a, int b) {
if (never)precalc();
int x = in[a];
int y = in[b];
if (x > y) { swap(x, y); }
int pos = rmq.query(x, y + 1);
int p = id[pos];
return disv[a] + disv[b] - disv[p] * 2;
}
/*@formatter:off*/
/*O(N) hldを使わず木を普通にたどる*/
void for_each_l(int u, int v, function<void(int)> fnode) { int r = lca(u, v); while (u != r) { fnode(u); u = par[u]; } while (v != r) { fnode(v); v = par[v]; } fnode(r); }
void for_each_edge_l/*O(N) 頂点に対しての処理順が可換*/(int u, int v, function<void(edge<int> &)> fedge) { int r = lca(u, v); auto sub = [&](int u, int r) { while (u != r) { forg(gi, g[u]) { if (t == par[u]) { fedge(g[u][gi]); u = par[u]; break; } } } }; sub(u, r); sub(v, r); }
/*Fは半開 (u,v)は木の頂点* /
/*中ではhldの頂点を見るため、seg木のupdateはhldのindexで行なう*/
void for_each_(int u, int v, const function<void(int, int)> &f) { if (never_hld)hld_build(); while (1) { if (vid[u] > vid[v]) swap(u, v); int l = max(vid[head[v]], vid[u]); int r = vid[v] + 1; f(l, r); if (head[u] != head[v]) v = par[head[v]]; else break; } }
void for_each_edge/*[l,r) O(log(N)) 辺を頂点として扱っている 上と同じ感じで使える*/(int u, int v, const function<void(int, int)> &f) { if (never_hld)hld_build(); while (1) { if (vid[u] > vid[v]) swap(u, v); if (head[u] != head[v]) { int l = vid[head[v]]; int r = vid[v] + 1; f(l, r); v = par[head[v]]; } else { if (u != v) { int l = vid[u] + 1; int r = vid[v] + 1; f(l, r); } break; } } }
int bel(int v) { /*hld内での頂点番号を返す*/ if (never_hld)hld_build(); return vid[v]; }
int bel(int f, int t) { /*辺のクエリを扱うときどの頂点に持たせればいいか(vidを返すのでそのままupd出来る)*/ if (never_hld)hld_build(); return hdep[f] > hdep[t] ? vid[f] : vid[t]; }
int bel(edge<T> &e) { /*辺のクエリを扱うときどの頂点に持たせればいいか(vidを返すのでそのままupd出来る)*/ if (never_hld)hld_build(); return hdep[e.f] > hdep[e.t] ? vid[e.f] : vid[e.t]; }
template<class ... U> int operator()(U ... args) { return bel(args...); }
};;
//辺によりメモリを大量消費ためedgesを消している
//頂点10^6でメモリを190MB(制限の8割)使う
//@formatter:off
//constexpr
int MOD = 1000000007;
struct mint { int x; mint() : x(0) {} mint(int a) { x = a % MOD; if (x < 0) x += MOD; } mint &operator+=(mint that) { x = (x + that.x) % MOD; return *this; } mint &operator-=(mint that) { x = (x + MOD - that.x) % MOD; return *this; } mint &operator*=(mint that) { x = (int) x * that.x % MOD; return *this; } mint &operator/=(mint that) { return *this *= that.inverse(); } mint operator-() { return mint(-this->x); } friend ostream &operator<<(ostream &out, mint m) { return out << m.x; } mint inverse() { int a = x, b = MOD, u = 1, v = 0; while (b) { int t = a / b; a -= t * b; u -= t * v; swap(a, b); swap(u, v); } return mint(u); } operator int() const { return x; } template<class T> mint &operator+=(T that) { return operator+=((mint) that); } template<class T> mint &operator-=(T that) { return operator-=((mint) that); } template<class T> mint &operator*=(T that) { return operator*=((mint) that); } template<class T> mint &operator/=(T that) { return operator/=(that); } mint operator+(mint that) { return mint(*this) += that; } mint operator-(mint that) { return mint(*this) -= that; } mint operator*(mint that) { return mint(*this) *= that; } mint operator/(mint that) { return mint(*this) /= that; } template<class T> mint operator+(T that) { return mint(*this) += (mint) that; } template<class T> mint operator-(T that) { return mint(*this) -= (mint) that; } template<class T> mint operator*(T that) { return mint(*this) *= (mint) that; } template<class T> mint operator/(T that) { return mint(*this) /= (mint) that; } bool operator==(mint that) const { return x == that.x; } bool operator==(signed that) const { return x == that; } bool operator!=(mint that) const { return x != that.x; } bool operator<(mint that) const { return x < that.x; } bool operator<=(mint that) const { return x <= that.x; } bool operator>(mint that) const { return x > that.x; } bool operator>=(mint that) const { return x >= that.x; }};
istream &operator>>(istream &i, mint &a) { i >> a.x; return i;}
typedef vector<mint> vm;
vector<mint> fac, finv;
int mint_len = 1400000; //既に変更されていたら変えない
void setmod(int mod = 1e9 + 7) { /*mint_len>=modの時fac[mint_len]が0になり、下の1/fac[mint_len]で0徐算になってしまう*/ if (mint_len >= mod - 1)mint_len = mod - 1; MOD = mod; fac = vector<mint>(mint_len + 1); finv = vector<mint>(mint_len + 1); fac[0] = 1; rep(i, 1, mint_len + 1) { fac[i] = fac[i - 1] * i; } finv[mint_len] = (mint) 1 / fac[mint_len]; rer(i, mint_len, 1) { finv[i - 1] = finv[i] * i; }}
mint com(int a, int b) { if (a < 0) return 0; if (b < 0 || b > a) return 0; return fac[a] * finv[a - b] * finv[b];}
mint hom(int a, int b) { return com(a + b - 1, b);}
template<typename T, typename U> mint mpow(const T a, const U b) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;}template<typename T> inline mint mpow(const T a, const mint b) { int x = a, res = 1; int p = b.x; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;}
using PM = pair<mint, mint>;
using vm = vector<mint>;
#define vvm(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(mint,__VA_ARGS__)
#define vnm(name, ...) auto name = make_v<mint>(__VA_ARGS__)
string yuri(const mint &a) { stringstream st; rep(i, 300) {rep(j, 300) {if ((mint) i / j == a) {st << i << " / " << j;return st.str();}}} rep(i, 1000) {rep(j, 1000) {if ((mint) i / j == a) {st << i << " / " << j;return st.str();}}} return st.str();}
#define smod setmod
//setmodを呼ぶ @formatter:on
ll hbit(ll n) {
n |= (n >> 1);
n |= (n >> 2);
n |= (n >> 4);
n |= (n >> 8);
n |= (n >> 16);
n |= (n >> 32);
return n - (n >> 1);
}
signed main() {
din(D, L, R, K);
setmod();
//1 index
tree<> g(bit(D), 1);
rep(i, 1, bit(D) - bit(D - 1)) {
g.add(i, i * 2);
g.add(i, i * 2 + 1);
}
int dl = log2(hbit(L));
int dr = log2(hbit(R));
//d(L) != d(R)
if (dl != dr) {
//l kotei
int rst = hbit(R);
mint cou = 0;
rep(r, rst, rst * 2) {
if (g.dis(L, r) == K) {
cou+=1;
}
}
mint res = 1;
rep(d, D) {
if (d != dr) {
res *= fac[bit(d)];
} else {
res *= fac[bit(d) - 1];
}
}
res *= cou;
cout << res << endl;
} else {
//l kotei
int rst = hbit(R);
mint cou = 0;
rep(r, rst, rst * 2) {
if (g.dis(L, r) == K) {
cou+=1;
}
}
mint res = 1;
rep(d, D) {
if (d != dr) {
res *= fac[bit(d)];
} else {
res *= fac[bit(d) - 2] * bit(d);
res *= cou;
}
}
cout << res << endl;
}
}