#include <bits/stdc++.h>
#ifdef LOCAL
#include <debug.hpp>
#else
#define debug(...) void(0)
#endif

template <class T> std::istream& operator>>(std::istream& is, std::vector<T>& v) {
    for (auto& e : v) {
        is >> e;
    }
    return is;
}

template <class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
    for (std::string_view sep = ""; const auto& e : v) {
        os << std::exchange(sep, " ") << e;
    }
    return os;
}

template <class T, class U = T> bool chmin(T& x, U&& y) {
    return y < x and (x = std::forward<U>(y), true);
}

template <class T, class U = T> bool chmax(T& x, U&& y) {
    return x < y and (x = std::forward<U>(y), true);
}

template <class T> void mkuni(std::vector<T>& v) {
    std::ranges::sort(v);
    auto result = std::ranges::unique(v);
    v.erase(result.begin(), result.end());
}

template <class T> int lwb(const std::vector<T>& v, const T& x) {
    return std::distance(v.begin(), std::ranges::lower_bound(v, x));
}

template <int MAX_W> struct F2Matrix {
    int H, W;

    std::vector<std::bitset<MAX_W>> A;

    F2Matrix(int H, int W) : H(H), W(W), A(H) {
        assert(W <= MAX_W);
        for (int i = 0; i < H; i++) A[i].reset();
    }

    bool empty() const { return A.empty(); }

    int size() const { return H; }

    int height() const { return H; }

    int width() const { return W; }

    inline const std::bitset<MAX_W>& operator[](int i) const { return A[i]; }

    inline std::bitset<MAX_W>& operator[](int i) { return A[i]; }

    static F2Matrix identity(int n) {
        F2Matrix res(n, n);
        for (int i = 0; i < n; i++) res[i][i] = 1;
        return res;
    }

    F2Matrix& operator+=(const F2Matrix& B) {
        assert(H == B.height() and W == B.width());
        for (int i = 0; i < H; i++) (*this)[i] ^= B[i];
        return *this;
    }

    F2Matrix& operator-=(const F2Matrix& B) { return *this += B; }

    F2Matrix& operator*=(const F2Matrix& B) {
        assert(W == B.height());
        F2Matrix C(H, B.width());
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                if (A[i][j]) {
                    C[i] ^= B[j];
                }
            }
        }
        std::swap(A, C.A);
        return *this;
    }

    F2Matrix operator+(const F2Matrix& B) const { return F2Matrix(*this) += B; }

    F2Matrix operator-(const F2Matrix& B) const { return F2Matrix(*this) -= B; }

    F2Matrix operator*(const F2Matrix& B) const { return F2Matrix(*this) *= B; }

    F2Matrix pow(long long n) const {
        assert(H == W);
        assert(0 <= n);
        F2Matrix x = *this, r = identity(H);
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }

    int rank() const { return F2Matrix(*this).gauss_jordan(); }

    int det() const {
        assert(H == W);
        return rank() == H ? 1 : 0;
    }

    F2Matrix inv() const {
        assert(height() == width());
        int n = height();
        F2Matrix B(*this), C = identity(n);
        for (int j = 0; j < n; j++) {
            int pivot = -1;
            for (int i = j; i < n; i++) {
                if (B[i][j]) {
                    pivot = i;
                    break;
                }
            }
            assert(pivot != -1);
            if (pivot != j) {
                std::swap(B[pivot], B[j]);
                std::swap(C[pivot], C[j]);
            }
            for (int i = 0; i < n; i++) {
                if (i != j and B[i][j]) {
                    B[i] ^= B[j];
                    C[i] ^= C[j];
                }
            }
        }
        return C;
    }

    std::vector<std::bitset<MAX_W>> system_of_linear_equations(const std::vector<bool>& b) {
        assert(W + 1 <= MAX_W);
        assert(int(b.size()) == H);
        F2Matrix B(*this);
        for (int i = 0; i < H; i++) B[i][W] = b[i];
        int rank = B.gauss_jordan(W);
        for (int i = rank; i < H; i++) {
            if (B[i][W]) {
                return {};
            }
        }
        std::vector<std::bitset<MAX_W>> res(1);
        std::vector<int> pivot(W, -1);
        for (int i = 0, j = 0; i < rank; i++) {
            while (not B[i][j]) j++;
            res[0][j] = B[i][W];
            pivot[j] = i;
        }
        for (int j = 0; j < W; j++) {
            if (pivot[j] != -1) continue;
            std::bitset<MAX_W> x;
            x[j] = 1;
            for (int k = 0; k < j; k++) {
                if (pivot[k] != -1) {
                    x[k] = B[pivot[k]][j];
                }
            }
            res.emplace_back(x);
        }
        return res;
    }

  private:
    int gauss_jordan(int pivot_end = -1) {
        if (empty()) return 0;
        if (pivot_end == -1) pivot_end = W;
        assert(pivot_end <= MAX_W);
        int rank = 0;
        for (int j = 0; j < pivot_end; j++) {
            int pivot = -1;
            for (int i = rank; i < H; i++) {
                if ((*this)[i][j]) {
                    pivot = i;
                    break;
                }
            }
            if (pivot == -1) continue;
            if (pivot != rank) std::swap((*this)[pivot], (*this)[rank]);
            for (int i = 0; i < H; i++) {
                if (i != rank and (*this)[i][j]) {
                    (*this)[i] ^= (*this)[rank];
                }
            }
            rank++;
        }
        return rank;
    }
};

using namespace std;

using ll = long long;

const int MAX_N = 1 << 8;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    int n, k;
    cin >> n >> k;
    vector<vector<int>> G(n);
    for (int i = 0; i < n - 1; i++) {
        int x, y;
        cin >> x >> y;
        x--, y--;
        G[x].emplace_back(y);
        G[y].emplace_back(x);
    }

    vector<bool> path(n, false);
    vector<vector<bool>> mat;
    vector<pair<int, int>> es;
    {
        path[0] = true;
        mat.emplace_back(path);
        es.emplace_back(-1, 0);
        path[0] = false;
    }
    auto dfs = [&](auto self, int v, int p, int d, int r) -> void {
        path[v] = true;
        if (d == k) {
            if (r < v) {
                mat.emplace_back(path);
                es.emplace_back(r, v);
            }
            path[v] = false;
            return;
        }
        for (int& u : G[v]) {
            if (u == p) continue;
            self(self, u, v, d + 1, r);
        }
        path[v] = false;
    };
    for (int i = 0; i < n; i++) dfs(dfs, i, -1, 0, i);

    int row = es.size();
    F2Matrix<MAX_N> M(row, n);
    for (int i = 0; i < row; i++) {
        for (int j = 0; j < n; j++) {
            M[i][j] = mat[i][j];
        }
    }

    int rank = 0;
    vector<int> ord(row);
    iota(ord.begin(), ord.end(), 0);
    for (int j = 0; j < n; j++) {
        int pivot = -1;
        for (int i = rank; i < row; i++) {
            if (M[i][j]) {
                pivot = i;
                break;
            }
        }
        if (pivot == -1) {
            cout << "NO" << endl;
            return 0;
        }
        if (pivot != rank) {
            swap(M[pivot], M[rank]);
            swap(ord[pivot], ord[rank]);
        }
        for (int i = 0; i < row; i++) {
            if (i != rank and M[i][j]) {
                M[i] ^= M[rank];
            }
        }
        rank++;
    }
    assert(ord[0] == 0);

    cout << "YES" << endl;
    cout << "! " << n - 1;
    for (int i = 1; i < n; i++) {
        auto [u, v] = es[ord[i]];
        cout << " " << u + 1 << " " << v + 1;
    }
    cout << endl;
    vector<int> w(n);
    w[0] = 0;
    for (int i = 1; i < n; i++) {
        cin >> w[i];
        assert(w[i] != -1);
    }
    F2Matrix<MAX_N> Mat(n, n);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            Mat[i][j] = mat[ord[i]][j];
        }
    }
    rank = 0;
    for (int j = 0; j < n; j++) {
        int pivot = -1;
        for (int i = rank; i < n; i++) {
            if (Mat[i][j]) {
                pivot = i;
                break;
            }
        }
        assert(pivot != -1);
        if (pivot != rank) swap(Mat[pivot], Mat[rank]);
        for (int i = 0; i < n; i++) {
            if (i != rank and Mat[i][j]) {
                Mat[i] ^= Mat[rank];
                w[i] ^= w[rank];
            }
        }
        rank++;
    }

    cout << "!";
    for (int i = 1; i < n; i++) cout << " " << w[i];
    cout << endl;
    return 0;
}