#include <stdio.h>
#define N 500000
#define INF 0x3f3f3f3f3f3f3f3fLL
#define MD 1000000007
#define H_ 19 /* H_ = ceil(log2(N * 2)) */
#define N_ (1 << H_)
long long min(long long a, long long b) { return a < b ? a : b; }
int max(int a, int b) { return a > b ? a : b; }
int mem[(N - 1) * 2], *ptr = mem, *ej[N], eo[N], n, k;
int ll[N], jj[N], ta[N], tb[N], kk[N + 1], qu[N * 2];
void dfs1(int p, int i, int d) {
int o;
kk[d + 1]++;
ll[i] = 0, jj[i] = -1;
for (o = eo[i]; o--; ) {
int j = ej[i][o];
if (j != p) {
dfs1(i, j, d + 1);
if (ll[i] < ll[j])
ll[i] = ll[j], jj[i] = j;
}
}
ll[i]++;
}
void dfs2(int p, int i, int d) {
static int time;
int o;
qu[ta[i] = time++] = i, tb[i] = kk[d]++;
if (jj[i] != -1)
dfs2(i, jj[i], d + 1);
else
time++;
for (o = eo[i]; o--; ) {
int j = ej[i][o];
if (j != p && j != jj[i])
dfs2(i, j, d + 1);
}
}
int cnt[N * 2]; long long xx[N + 1];
void get_range(int a, int *l, int *r) {
*l = tb[qu[a]], *r = *l + cnt[a];
}
void dfs3(int p, int i) {
int o, d, l1, r1, l2, r2;
long long c;
for (o = eo[i]; o--; ) {
int j = ej[i][o];
if (j != p)
dfs3(i, j);
}
if (k <= ll[i]) {
get_range(ta[i] + k - 1, &l1, &r1);
xx[l1]++, xx[r1]--;
if (p != -1)
xx[tb[p]] -= r1 - l1, xx[tb[p] + 1] += r1 - l1;
}
cnt[ta[i]]++;
for (o = eo[i]; o--; ) {
int j = ej[i][o];
if (j != p && j != jj[i]) {
for (d = 1; d <= ll[j] && d < k; d++)
if (k - d <= ll[i]) {
get_range(ta[i] + k - d - 1, &l1, &r1), get_range(ta[j] + d - 1, &l2, &r2);
c = (long long) (r1 - l1) * (r2 - l2);
xx[l1] += r2 - l2, xx[r1] -= r2 - l2;
xx[l2] += r1 - l1, xx[r2] -= r1 - l1;
xx[tb[i]] -= c, xx[tb[i] + 1] += c;
if (p != -1)
xx[tb[p]] -= c, xx[tb[p] + 1] += c;
}
for (d = 1; d <= ll[j]; d++)
cnt[ta[i] + d] += cnt[ta[j] + d - 1];
}
}
}
long long ww[N];
void dfs4(int p, int i) {
int o;
ww[i] = xx[tb[i]];
for (o = eo[i]; o--; ) {
int j = ej[i][o];
if (j != p) {
dfs4(i, j);
ww[i] += ww[j];
}
}
}
int h_, n_;
long long stu[N_ * 2], lzu[N_]; int stv[N_ * 2], lzv[N_];
void put(int i, long long u, long long v) {
if (stu[i] != INF && u != INF)
stu[i] += u, stv[i] = (long long) stv[i] * v % MD;
else
stu[i] = INF, stv[i] = 0;
if (i < n_) {
if (lzu[i] != INF && u != INF)
lzu[i] += u, lzv[i] = (long long) lzv[i] * v % MD;
else
lzu[i] = INF, lzv[i] = 0;
}
}
void pus(int i) {
if (lzu[i] != 0 || lzv[i] != 1)
put(i << 1 | 0, lzu[i], lzv[i]), put(i << 1 | 1, lzu[i], lzv[i]), lzu[i] = 0, lzv[i] = 1;
}
void pul(int i) {
if (lzu[i] == 0 && lzv[i] == 1) {
int l = i << 1, r = l | 1;
if (stu[l] < stu[r])
stu[i] = stu[l], stv[i] = stv[l];
else if (stu[l] > stu[r])
stu[i] = stu[r], stv[i] = stv[r];
else
stu[i] = stu[l], stv[i] = (stv[l] + stv[r]) % MD;
}
}
void push(int i) {
int h;
for (h = h_; h > 0; h--)
pus(i >> h);
}
void pull(int i) {
while (i > 1)
pul(i >>= 1);
}
void upd(int i, long long u, int v) {
push(i += n_);
stu[i] = u, stv[i] = v;
pull(i);
}
void update(int l, int r, long long u, int v) {
if (l <= r) {
int l_ = l += n_, r_ = r += n_;
push(l_), push(r_);
for ( ; l <= r; l >>= 1, r >>= 1) {
if ((l & 1) == 1)
put(l++, u, v);
if ((r & 1) == 0)
put(r--, u, v);
}
pull(l_), pull(r_);
}
}
void query(int l, int r, long long *u_, int *v_) {
long long u = INF, v = 0;
if (l <= r) {
push(l += n_), push(r += n_);
for ( ; l <= r; l >>= 1, r >>= 1) {
if ((l & 1) == 1) {
if (u > stu[l])
u = stu[l], v = 0;
if (u == stu[l])
v = (v + stv[l]) % MD;
l++;
}
if ((r & 1) == 0) {
if (u > stu[r])
u = stu[r], v = 0;
if (u == stu[r])
v = (v + stv[r]) % MD;
r--;
}
}
}
*u_ = u, *v_ = v;
}
void process(int i, int j, int d) {
long long u1, ui, uj, u;
int v1, vi, vj, v;
u1 = INF, v1 = 0;
query(ta[i] + d, ta[i] + d, &ui, &vi);
query(ta[j], ta[j] + min(ll[j], min(k - d - 1, d - 2)), &uj, &vj);
u = ui + uj;
v = (long long) vi * vj % MD;
if (u1 > u)
u1 = u, v1 = 0;
if (u1 == u)
v1 = (v1 + v) % MD;
if (d - 1 <= ll[j]) {
query(ta[j] + d - 1, ta[j] + d - 1, &uj, &vj);
query(ta[i] + 1, ta[i] + min(k - d, d), &ui, &vi);
u = ui + uj;
v = (long long) vi * vj % MD;
if (u1 > u)
u1 = u, v1 = 0;
if (u1 == u)
v1 = (v1 + v) % MD;
}
upd(ta[i] + d, u1, v1);
}
void dfs5(int p, int i) {
int o, j, d;
long long u;
int v;
upd(ta[i] + 0, ww[i], 1);
if (jj[i] == -1)
upd(ta[i] + 1, 0, 1);
else {
for (o = eo[i]; o--; ) {
j = ej[i][o];
if (j != p)
dfs5(i, j);
}
j = jj[i];
query(ta[j], ta[j] + ll[j], &u, &v);
update(ta[i] + 0, ta[i] + 0, u, v);
if (ll[i] >= k)
upd(ta[i] + k, INF, 0);
for (o = eo[i]; o--; ) {
j = ej[i][o];
if (j != p && j != jj[i]) {
int lower, upper;
query(ta[j], ta[j] + ll[j], &u, &v);
update(ta[i] + 0, ta[i] + 0, u, v);
lower = ll[j] + 2, upper = min(ll[i], k - 1 - ll[j]);
if (lower > upper)
for (d = min(ll[i], k); d > 0; d--)
process(i, j, d);
else {
for (d = min(ll[i], k); d > upper; d--)
process(i, j, d);
query(ta[j], ta[j] + ll[j], &u, &v);
update(ta[i] + lower, ta[i] + upper, u, v);
for (d = lower - 1; d > 0; d--)
process(i, j, d);
}
}
}
}
}
int main() {
static int ii_[N - 1], jj_[N - 1];
int h, i, j, d, v;
long long w, u;
scanf("%d%d", &n, &k);
for (h = 0; h < n - 1; h++) {
scanf("%d%d", &i, &j), i--, j--;
ii_[h] = i, jj_[h] = j;
eo[i]++, eo[j]++;
}
for (i = 0; i < n; i++) {
ej[i] = ptr, ptr += eo[i];
eo[i] = 0;
}
for (h = 0; h < n - 1; h++) {
i = ii_[h], j = jj_[h];
ej[i][eo[i]++] = j, ej[j][eo[j]++] = i;
}
dfs1(-1, 0, 0);
for (d = 1; d <= n; d++)
kk[d] += kk[d - 1];
dfs2(-1, 0, 0);
dfs3(-1, 0);
for (i = 1; i <= n; i++)
xx[i] += xx[i - 1];
dfs4(-1, 0);
w = 0;
for (i = 0; i < n; i++)
w += ww[i];
w /= k;
h_ = 0;
while (1 << h_ < n * 2)
h_++;
n_ = 1 << h_;
for (i = 0; i < n_; i++)
lzv[i] = 1;
dfs5(-1, 0);
query(ta[0], ta[0] + ll[0], &u, &v);
if (u == w)
printf("YES\n%d\n", v);
else
printf("NO\n0\n");
return 0;
}
