// URL: https://yukicoder.me/problems/no/196 import std.algorithm, std.array, std.bitmanip, std.container, std.conv, std.format, std.functional, std.math, std.range, std.traits, std.typecons, std.stdio, std.string; version(unittest) {} else void main() { int N, K; io.getV(N, K); auto g = Graph(N); foreach (_; 0..N-1) { int a, b; io.getV(a, b); g.addEdgeB(a, b); } auto t = g.tree(0); auto c = new mint[][](N); foreach_reverse (u; t.dfsOrder) { auto children = t.children(u).array, nv = children.length; auto ss = 0, dp = new mint[][](nv+1); dp[0] = [mint(1)]; foreach (i, v; children) { auto s = t.size[v], pss = ss; ss += s; dp[i+1] = new mint[](ss+1); foreach (j; 0..ss+1) foreach (k; max(0, j-pss)..min(s, j)+1) dp[i+1][j] += dp[i][j-k] * c[v][k]; } c[u] = dp[$-1]; c[u] ~= mint(1); } io.put(c[0][K]); } struct Graph { alias Node = int; Node n; Node[][] g; alias g this; pure nothrow @safe { this(Node n) { this.n = n; g = new Node[][](n); } void addEdge(Node u, Node v) in { assert(0 <= u && u < n && 0 <= v && v < n); } do { g[u] ~= v; } void addEdgeB(Node u, Node v) in { assert(0 <= u && u < n && 0 <= v && v < n); } do { g[u] ~= v; g[v] ~= u; } } } struct GraphW(W = int, W i = 10^^9) { alias Node = int, Wt = W, inf = i; struct Edge { Node src, dst; Wt wt; alias cap = wt; } Node n; Edge[][] g; alias g this; pure nothrow @safe { this(Node n) { this.n = n; g = new Edge[][](n); } void addEdge(Node u, Node v, Wt w) in { assert(0 <= u && u < n && 0 <= v && v < n); } do { g[u] ~= Edge(u, v, w); } void addEdgeB(Node u, Node v, Wt w) in { assert(0 <= u && u < n && 0 <= v && v < n); } do { g[u] ~= Edge(u, v, w); g[v] ~= Edge(v, u, w); } } } struct GraphM(W = int, W i = 10^^9) { alias Node = int, Wt = W, inf = i; Node n; Wt[][] g; alias g this; pure nothrow @safe { this(int n) { this.n = n; g = new Wt[][](n, n); } static GraphM!(W, i) init(Node n) { auto g = GraphM!(W, i)(n); foreach (i; 0..n) { g[i][] = inf; g[i][i] = 0; } return g; } } } struct Tree(Graph) { alias Node = Graph.Node; Graph g; alias g this; Node root; Node[] parent, dfsOrder; int[] size, depth; pure nothrow @safe { this(Graph g, Node r) in { assert(0 <= r && r < g.n); } do { this.g = g; this.root = r; parent = new Node[](n); depth = new int[](n); depth[] = -1; auto st = SList!UP(UP(r, r)); while (!st.empty) { auto up = st.front; st.removeFront(); parent[up.u] = up.p; depth[up.u] = depth[up.p] + 1; dfsOrder ~= up.u; foreach (v; g[up.u]) if (v != up.p) st.insertFront(UP(v, up.u)); } size = new int[](n); size[] = 1; foreach_reverse (u; dfsOrder.drop(1)) size[parent[u]] += size[u]; } auto children(Node u) const in { assert(0 <= u && u < g.n); } do { return g[u].filter!(v => v != parent[u]); } } private { struct UP { Node u, p; } } } pure nothrow @safe { auto tree(Graph, Node)(Graph g, Node r) in { assert(0 <= r && r < g.n); } do { return Tree!Graph(g, r); } } const mod = 10^^9+7; alias mint = ModInt!mod; pure nothrow @safe { T powr(alias pred = "a*b", T, U)(const T a, U n, T one) if (isIntegral!U) { auto b = T(a); alias predFun = binaryFun!pred; if (n == 0) return one; auto r = one; for (; n > 0; n >>= 1) { if (n&1) r = predFun(r, b); b = predFun(b, b); } return r; } T powr(alias pred = "a*b", T, U)(const T a, U n) if (isIntegral!U) { return powr!(pred, T, U)(a, n, T(1)); } } pure nothrow @nogc @safe { auto lowerBoundBy(alias conv = "a", alias comp = "a tuple(e, convFun(e))).assumeSorted!((a, b) => compFun(a[1], b[1])); } } pure nothrow @nogc @safe { T cdiv(T)(const T a, const T b) { return (a+b-1)/b; } T pmod(T)(const T a, const T b) { return a >= 0 ? a%b : a%b+b; } ExtGcdResult!T extGcd(T)(const T a, const T b) { if (a == 0) { return ExtGcdResult!T(T(b), T(0), T(1)); } else { auto r = extGcd(b%a, a); return ExtGcdResult!T(r.gcd, r.y-(b/a)*r.x, r.x); } } private struct ExtGcdResult(T) { T gcd, x, y; } } struct ModInt(int m, bool pos = false) { pure nothrow @nogc @safe { @property int value() { return i; } @property void value(int v) { i = nm(v); } alias value this; this(T)(T v) if (isIntegral!T) { i = nm(v); } this(ref return scope const Mint v) { i = v.i; } ref Mint opAssign(T)(T v) if (isIntegral!T) { i = nm(v); return this; } ref Mint opAssign(const Mint v) { i = v.i; return this; } static if (!pos) { Mint opUnary(string op: "-")() const { return Mint(-i); } } static if (m < int.max / 2) { Mint opBinary(string op, T)(T r) const if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { return Mint(mixin("i"~op~"r")); } ref Mint opOpAssign(string op, T)(T r) if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { i = nm(mixin("i"~op~"r")); return this; } } else { Mint opBinary(string op, T)(T r) const if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { return Mint(mixin("l"~op~"r")); } ref Mint opOpAssign(string op, T)(T r) if ((op == "+" || (!pos && op == "-")) && isIntegral!T) { i = nm(mixin("l"~op~"r")); return this; } } Mint opBinary(string op: "*", T)(T r) const if (isIntegral!T) { return Mint(l*r); } ref Mint opOpAssign(string op: "*", T)(T r) if (isIntegral!T) { i = nm(l*r); return this; } Mint opBinary(string op)(const Mint r) const if (op == "+" || !pos && op == "-" || op == "*") { return opBinary!op(r.i); } ref Mint opOpAssign(string op)(const Mint r) if (op == "+"|| !pos && op == "-" || op == "*") { return opOpAssign!op(r.i); } Mint opBinary(string op: "^^", T)(T n) if (isIntegral!T) { return powr(this, n, Mint(1)); } static if (!pos) { Mint opBinary(string op: "/")(const Mint r) const { return Mint(l*r.inv.i); } ref Mint opOpAssign(string op: "/")(const Mint r) { i = nm(l*r.inv.i); return this; } Mint opBinary(string op: "/", T)(T r) const if (isIntegral!T) { return opBinary!op(Mint(r)); } Mint opOpAssign(string op: "/", T)(T r) if (isIntegral!T) { return opOpAssign!op(Mint(r)); } Mint inv() const { return Mint(extGcd(i, m).x); } } } private { alias Mint = ModInt!(m, pos); version(BigEndian) union { long l; struct { int i2; int i; } } else union { long l; int i; } pure nothrow @nogc @safe { int nm(T)(T v) const if (isIntegral!T) { static if (pos) return cast(int)(v%m); else return cast(int)pmod(v, m); } } } } auto io = IO!()(); import std.stdio; struct IO(alias IN = stdin, alias OUT = stdout) { import std.meta : allSatisfy; import core.stdc.stdlib : exit; void getV(T...)(ref T v) { foreach (ref w; v) get(w); } void getA(T)(size_t n, ref T v) if (hasAssignableElements!T) { v = new T(n); foreach (ref w; v) get(w); } void getC(T...)(size_t n, ref T v) if (allSatisfy!(hasAssignableElements, T)) { foreach (ref w; v) w = new typeof(w)(n); foreach (i; 0..n) foreach (ref w; v) get(w[i]); } void getM(T)(size_t r, size_t c, ref T v) if (hasAssignableElements!T && hasAssignableElements!(ElementType!T)) { v = new T(r); foreach (ref w; v) getA(c, w); } template getS(E...) { void getS(T)(size_t n, ref T v) { v = new T(n); foreach (ref w; v) foreach (e; E) mixin("get(w."~e~");"); } } const struct PutConf { bool newline = true, flush, exit; string floatFormat = "%.10f", delimiter = " "; } void put(alias conf = "{}", T...)(T v) { mixin("const PutConf c = "~conf~"; putMain!c(v);"); } void putB(alias conf = "{}", S, T)(bool c, S t, T f) { if (c) put!conf(t); else put!conf(f); } void putRaw(T...)(T v) { OUT.write(v); OUT.writeln; } private { dchar[] buf; auto sp = (new dchar[](0)).splitter; void nextLine() { IN.readln(buf); sp = buf.splitter; } void get(T)(ref T v) { if (sp.empty) nextLine(); v = sp.front.to!T; sp.popFront(); } void putMain(PutConf c, T...)(T v) { foreach (i, w; v) { putOne!c(w); if (i+1 < v.length) OUT.write(c.delimiter); } static if (c.newline) OUT.writeln; static if (c.flush) OUT.flush(); static if (c.exit) exit(0); } void putOne(PutConf c, T)(T v) { static if (isInputRange!T && !isSomeString!T) putRange!c(v); else static if (isFloatingPoint!T) OUT.write(format(c.floatFormat, v)); else static if (hasMember!(T, "fprint")) v.fprint(OUT); else OUT.write(v); } void putRange(PutConf c, T)(T v) { auto w = v; while (!w.empty) { putOne!c(w.front); w.popFront(); if (!w.empty) OUT.write(c.delimiter); } } } }