We have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i. For each k=1, ..., N, solve the problem below:

* Consider writing a number on each vertex in the tree in the following manner:
* First, write 1 on Vertex k.
* Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows:
* Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.
* Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq a_i,b_i \leq N
* The given graph is a tree.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1
:
a_{N-1} b_{N-1}


Output

For each k=1, 2, ..., N in this order, print a line containing the answer to the problem.

Examples

Input

3
1 2
1 3


Output

2
1
1


Input

2
1 2


Output

1
1


Input

5
1 2
2 3
3 4
3 5


Output

2
8
12
3
3


Input

8
1 2
2 3
3 4
3 5
3 6
6 7
6 8


Output

40
280
840
120
120
504
72
72
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.function.IntBinaryOperator;

public class Main {
    private static final Mod mod = new Mod(1_000_000_007);

    static void solve(MyScanner in, MyWriter out) {
        int n = in.nextInt();
        int[][] ab = in.nextVerticalIntArrays(2, n - 1);
        int[] a = decrement(ab[0]);
        int[] b = decrement(ab[1]);
        List<Edge> edges = Edge.listOf(a, b);
        AdjacencyList tree = AdjacencyList.forUndirectedGraph(n, edges);
        int[] sizes = subtreeSizes(tree, 0);
        ModCombination c = new ModCombination(mod.divisor, n);
        long[] cases = calcCases(tree, c, sizes, 0);
        long[] answer = reroot(tree, c, sizes, cases, 0);
        out.joinAndPrintln(answer, System.lineSeparator());
    }
    static long[] reroot(AdjacencyList tree,
                         ModCombination c,
                         int[] sizes,
                         long[] cases,
                         int rootId) {
        long[] result = new long[tree.vertexCount()];
        result[rootId] = cases[rootId];
        _reroot(result, tree, c, sizes, sizes[rootId], cases, rootId, -1);
        return result;
    }
    static void _reroot(long[] result,
                        AdjacencyList tree,
                        ModCombination c,
                        int[] sizes,
                        int treeSize,
                        long[] cases,
                        int id,
                        int parent) {
        if (parent >= 0) {
            result[id] = mod.value(result[parent])
                            .div(c.of(treeSize - 1, sizes[id]))
                            .multiply(c.of(treeSize - 1, treeSize - sizes[id]))
                            .longValue();
        }
        for (Edge e : tree.edgesFrom(id)) {
            if (e.to == parent) {
                continue;
            }
            _reroot(result, tree, c, sizes, treeSize, cases, e.to, id);
        }
    }
    static long[] calcCases(AdjacencyList tree,
                            ModCombination c,
                            int[] sizes,
                            int rootId) {
        long[] result = new long[tree.vertexCount()];
        _calcCases(result, tree, c, sizes, rootId, -1);
        return result;
    }
    static long _calcCases(long[] result,
                           AdjacencyList tree,
                           ModCombination c,
                           int[] sizes,
                           int id,
                           int parent) {
        Mod.Value cases = mod.value(1);
        int n = sizes[id] - 1;
        for (Edge e : tree.edgesFrom(id)) {
            if (e.to == parent) {
                continue;
            }
            cases.multiply(c.of(n, sizes[e.to]))
                 .multiply(_calcCases(result, tree, c, sizes, e.to, id));
            n -= sizes[e.to];
        }
        return result[id] = cases.longValue();
    }
    static int[] subtreeSizes(AdjacencyList tree, int rootId) {
        int[] result = new int[tree.vertexCount()];
        IntBinaryOperator[] f = new IntBinaryOperator[1];
        f[0] = (id, parent) -> {
            int count = 1;
            for (Edge e : tree.edgesFrom(id)) {
                if (e.to != parent) {
                    count += f[0].applyAsInt(e.to, id);
                }
            }
            return result[id] = count;
        };
        f[0].applyAsInt(rootId, -1);
        return result;
    }
    static final class ModCombination {
        final int divisor;
        final int maxN;
        private final long[] factorial;
        private final long[] factorialInverse;

        ModCombination(int divisor, int maxN) {
            if (divisor <= 0 || maxN < 0) {
                throw new IllegalArgumentException();
            }
            this.divisor = divisor;
            this.maxN = maxN;
            factorial = new long[Math.max(2, maxN + 1)];
            long[] inverse = new long[factorial.length];
            factorialInverse = new long[factorial.length];

            factorial[0] = factorial[1] = 1;
            inverse[1] = 1;
            factorialInverse[0] = factorialInverse[1] = 1;
            for (int i = 2; i < factorial.length; i++) {
                factorial[i] = factorial[i - 1] * i % divisor;
                inverse[i] = divisor
                             - inverse[divisor % i] * (divisor / i) % divisor;
                factorialInverse[i] =
                        factorialInverse[i - 1] * inverse[i] % divisor;
            }
        }
        long of(int n, int k) {
            if (n > maxN) {
                throw new IllegalArgumentException();
            }
            if (k > n) {
                return 0;
            }
            return factorial[n]
                   * (factorialInverse[k] * factorialInverse[n - k] % divisor)
                   % divisor;
        }
    }
    static final class Mod {
        final int divisor;

        Mod(int divisor) {
            if (divisor <= 0) {
                throw new IllegalArgumentException();
            }
            this.divisor = divisor;
        }
        long mod(long dividend) {
            return Math.floorMod(dividend, divisor);
        }
        long add(long a, long b) {
            return mod(mod(a) + mod(b));
        }
        long subtract(long a, long b) {
            return mod(mod(a) - mod(b));
        }
        long multiply(long a, long b) {
            return mod(mod(a) * mod(b));
        }
        long pow(long a, long b) {
            if (b < 0) {
                throw new IllegalArgumentException();
            }
            long r = 1;
            while (b > 0) {
                if ((b & 1) == 1) {
                    r = multiply(r, a);
                }
                a = multiply(a, a);
                b >>= 1;
            }
            return r;
        }
        long inverse(long a) {
            // assert isCoprime(a, divisor);
            if (a == 0) {
                throw new IllegalArgumentException();
            }
            a = mod(a);
            long b = divisor;
            long u = 1;
            long v = 0;
            while (b != 0) {
                long q = a / b;
                a -= q * b;
                u -= q * v;

                long tmp = a;
                a = b;
                b = tmp;

                tmp = u;
                u = v;
                v = tmp;
            }
            return mod(u);
        }
        long div(long a, long b) {
            return multiply(a, inverse(b));
        }
        Value value(long initialValue) {
            return new Value(this, initialValue);
        }

        static final class Value {
            private final Mod mod;
            private long value;

            private Value(Mod mod, long initialValue) {
                this.mod = mod;
                value = mod.mod(initialValue);
            }
            long longValue() {
                return value;
            }
            Value add(long a) {
                value = mod.add(value, a);
                return this;
            }
            Value add(Value a) {
                return add(a.value);
            }
            Value subtract(long a) {
                value = mod.subtract(value, a);
                return this;
            }
            Value subtract(Value a) {
                return subtract(a.value);
            }
            Value multiply(long a) {
                value = mod.multiply(value, a);
                return this;
            }
            Value multiply(Value a) {
                return multiply(a.value);
            }
            Value pow(long a) {
                value = mod.pow(value, a);
                return this;
            }
            Value inverse() {
                value = mod.inverse(value);
                return this;
            }
            Value div(long a) {
                value = mod.div(value, a);
                return this;
            }
            Value div(Value a) {
                return div(a.value);
            }
            @Override
            public String toString() {
                return Long.toString(value);
            }
        }
    }
    private static int[] decrement(int[] a) {
        for (int i = 0; i < a.length; i++) {
            a[i]--;
        }
        return a;
    }
    static final class Edge {
        final int from;
        final int to;
        final long weight;
        final int id;

        Edge(int from, int to) {
            this(from, to, 1);
        }
        Edge(int from, int to, int weight) {
            this(from, to, weight, -1);
        }
        Edge(int from, int to, long weight, int id) {
            if (from < 0 || to < 0) {
                throw new IllegalArgumentException();
            }
            this.from = from;
            this.to = to;
            this.weight = weight;
            this.id = id;
        }
        int from() {
            return from;
        }
        int to() {
            return to;
        }
        long weight() {
            return weight;
        }
        Edge reverse() {
            return new Edge(to, from, weight, id);
        }
        static List<Edge> listOf(int[] from, int[] to) {
            return listOf(from, to, null);
        }
        static List<Edge> listOf(int[] from, int[] to, int[] weight) {
            if (from.length != to.length
                || (weight != null && from.length != weight.length)) {
                throw new IllegalArgumentException();
            }
            List<Edge> result = new ArrayList<>(from.length);
            for (int i = 0; i < from.length; i++) {
                result.add(new Edge(from[i],
                                    to[i],
                                    weight == null ? 1 : weight[i],
                                    i));
            }
            return result;
        }
    }
    static final class AdjacencyList {
        private final List<List<Edge>> list;

        private AdjacencyList(List<List<Edge>> list) {
            this.list = list;
        }
        int vertexCount() {
            return list.size();
        }
        List<Edge> edgesFrom(int vertexId) {
            return list.get(vertexId);
        }
        static AdjacencyList forDirectedGraph(int vertexCount,
                                              List<Edge> edges) {
            List<List<Edge>> list =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            list.replaceAll(e -> new ArrayList<>());
            for (Edge e : edges) {
                list.get(e.from).add(e);
            }
            return new AdjacencyList(list);
        }
        static AdjacencyList forUndirectedGraph(int vertexCount,
                                                List<Edge> edges) {
            List<List<Edge>> list =
                    new ArrayList<>(Collections.nCopies(vertexCount, null));
            list.replaceAll(e -> new ArrayList<>());
            for (Edge e : edges) {
                list.get(e.from).add(e);
                list.get(e.to).add(e.reverse());
            }
            return new AdjacencyList(list);
        }
    }
    public static void main(String[] args) {
        MyWriter w = new MyWriter(System.out);
        solve(new MyScanner(System.in), w);
        w.flush();
    }
    static final class MyScanner {
        static final int BUFFER_SIZE = 8192;
        private final InputStream in;
        private final byte[] buffer = new byte[BUFFER_SIZE];
        private int point;
        private int readLength;

        MyScanner(InputStream in) {
            this.in = in;
        }
        private byte readByte() {
            if (point < readLength) {
                byte result = buffer[point];
                point += 1;
                return result;
            }
            try {
                readLength = in.read(buffer);
            } catch (IOException e) {
                throw new AssertionError(null, e);
            }
            if (readLength == -1) {
                return -1;
            }
            point = 1;
            return buffer[0];
        }
        private static boolean isPrintableCharExceptSpace(byte c) {
            return 33 <= c && c <= 126;
        }
        public char nextChar() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            return (char)c;
        }
        public String next() {
            return next(16);
        }
        public String next(int n) {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            StringBuilder b = new StringBuilder(n);
            do {
                b.append((char)c);
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return b.toString();
        }
        public long nextLong() {
            byte c = readByte();
            while (!(c == -1 || isPrintableCharExceptSpace(c))) {
                c = readByte();
            }
            if (c == -1) {
                throw new NoSuchElementException();
            }
            boolean minus = false;
            if (c == '-') {
                minus = true;
                c = readByte();
            }
            long result = 0L;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                result = result * 10L + (c - '0');
                c = readByte();
            } while (c != -1 && isPrintableCharExceptSpace(c));
            return minus ? -result : result;
        }
        public int nextInt() {
            long n = nextLong();
            if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
                throw new InputMismatchException();
            }
            return (int)n;
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
        public int[] nextIntArray(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextInt();
            }
            return result;
        }
        public long[] nextLongArray(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextLong();
            }
            return result;
        }
        public char[] nextCharArray(int n) {
            char[] result = new char[n];
            for (int i = 0; i < n; i++) {
                result[i] = nextChar();
            }
            return result;
        }
        public char[][] next2dCharArray(int n, int m) {
            char[][] result = new char[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    result[i][j] = nextChar();
                }
            }
            return result;
        }
        public int[][] nextVerticalIntArrays(int arrayCount, int arrayLength) {
            int[][] result = new int[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextInt();
                }
            }
            return result;
        }
        public long[][] nextVerticalLongArrays(int arrayCount,
                                               int arrayLength) {
            long[][] result = new long[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextLong();
                }
            }
            return result;
        }
        public char[][] nextVerticalCharArrays(int arrayCount,
                                               int arrayLength) {
            char[][] result = new char[arrayCount][arrayLength];
            for (int i = 0; i < arrayLength; i++) {
                for (int j = 0; j < arrayCount; j++) {
                    result[j][i] = nextChar();
                }
            }
            return result;
        }
    }
    static final class MyWriter extends PrintWriter {
        MyWriter(OutputStream out) {
            super(out);
        }
        public void joinAndPrintln(int[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(int[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(long[] x) {
            joinAndPrintln(x, " ");
        }
        public void joinAndPrintln(long[] x, String delimiter) {
            StringBuilder b = new StringBuilder();
            if (x.length > 0) {
                b.append(x[0]);
                for (int i = 1; i < x.length; i++) {
                    b.append(delimiter).append(x[i]);
                }
            }
            println(b.toString());
        }
        public void joinAndPrintln(Iterable<?> iterable) {
            joinAndPrintln(iterable, " ");
        }
        public void joinAndPrintln(Iterable<?> iterable, String delimiter) {
            StringBuilder b = new StringBuilder();
            for (Iterator<?> i = iterable.iterator(); i.hasNext();) {
                b.append(i.next());
                while (i.hasNext()) {
                    b.append(delimiter).append(i.next());
                }
            }
            println(b.toString());
        }
    }
}
