//#pragma GCC optimize ("-O3") #include 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; #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; using vb = vector; using vs = vector; using vd = vector; using vc = vector; using vp = vector

; using vt = vector; #define vec vector #define o_vvt(o1, o2, o3, o4, name, ...) name #define vvt0(t) vec> #define vvt1(t, a) vec>a #define vvt2(t, a, b) vec>a(b) #define vvt3(t, a, b, c) vec> a(b,vec(c)) #define vvt4(t, a, b, c, d) vec> a(b,vec(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 vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a, make_v(ts...)); } #define vni(name, ...) auto name = make_v(__VA_ARGS__) #define vnb(name, ...) auto name = make_v(__VA_ARGS__) #define vns(name, ...) auto name = make_v(__VA_ARGS__) #define vnd(name, ...) auto name = make_v(__VA_ARGS__) #define vnc(name, ...) auto name = make_v(__VA_ARGS__) #define vnp(name, ...) auto name = make_v

(__VA_ARGS__) #define v3i(a, b, c, d) vector> a(b, vector(c, vi(d))) #define v3d(a, b, c, d) vector> a(b, vector(c, vd(d))) #define v3m(a, b, c, d) vector> a(b, vector(c, vm(d))) #define _vvi vector #define _vvl vector #define _vvb vector #define _vvs vector #define _vvd vector #define _vvc vector #define _vvp vector #define PQ priority_queue, greater > #define tos to_string using mapi = map; using mapd = map; using mapc = map; using maps = map; using seti = set; using setd = set; using setc = set; using sets = set; using qui = queue; #define bset bitset #define uset unordered_set #define mset multiset #define umap unordered_map #define umapi unordered_map #define umapp unordered_map #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::min(); ll mi = numeric_limits::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 inline void sort(vector &a) { sort(a.begin(), a.end()); }; template inline void sort(vector &a, int len) { sort(a.begin(), a.begin() + len); }; template inline void sort(vector &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

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 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::g; using undigraph::n; using undigraph::edges; using undigraph::usedv; vector disv; vector dep, par; vector 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(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 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 &)> 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 &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 &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 &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 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 mint &operator+=(T that) { return operator+=((mint) that); } template mint &operator-=(T that) { return operator-=((mint) that); } template mint &operator*=(T that) { return operator*=((mint) that); } template 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 mint operator+(T that) { return mint(*this) += (mint) that; } template mint operator-(T that) { return mint(*this) -= (mint) that; } template mint operator*(T that) { return mint(*this) *= (mint) that; } template 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 vm; vector 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_len + 1); finv = vector(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 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 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; using vm = vector; #define vvm(...) o_vvt(__VA_ARGS__,vvt4,vvt3,vvt2 ,vvt1,vvt0)(mint,__VA_ARGS__) #define vnm(name, ...) auto name = make_v(__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; } }