Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**8)

def solve():
    N = int(input())
    AB = [tuple(map(int,input().split())) for i in range(N-1)]
    MOD = 10**9+7
    es = [[] for _ in range(N)]
    for a,b in AB:
        a,b = a-1,b-1
        es[a].append(b)
        es[b].append(a)

    cs = [1] * N
    def dfs(v,p=-1):
        ret = 1
        for to in es[v]:
            if to==p: continue
            ret += dfs(to,v)
        cs[v] = ret
        return ret
    dfs(0)
    ans = 0
    for i in range(N):
        if len(es[i]) == 1: continue
        ans += pow(2,N-1,MOD) - 1
        c = 0
        for to in es[i]:
            if cs[to] > cs[i]: continue
            c += cs[to]
            ans -= pow(2,cs[to],MOD) - 1
        ans -= pow(2,N-c-1,MOD) - 1

    ans *= pow(pow(2,N,MOD), MOD-2, MOD)
    print(ans%MOD)
solve()

Fixed submission:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**8)

def solve():
    N = int(input())
    AB = [tuple(map(int,input().split())) for i in range(N-1)]
    MOD = 10**9+7
    es = [[] for _ in range(N)]
    for a,b in AB:
        a,b = a-1,b-1
        es[a].append(b)
        es[b].append(a)

    cs = [1] * N
    def dfs(v,p=-1):
        ret = 1
        for to in es[v]:
            if to==p: continue
            ret += dfs(to,v)
        cs[v] = ret
        return ret
    dfs(0)

    pow2 = [1]
    for i in range(N):
        pow2.append((pow2[-1]*2) % MOD)

    ans = 0
    for i in range(N):
        if len(es[i]) == 1: continue
        ans += pow2[N-1] - 1
        c = 0
        for to in es[i]:
            if cs[to] > cs[i]: continue
            c += cs[to]
            ans -= pow2[cs[to]] - 1
        ans -= pow2[N-c-1] - 1

    ans *= pow(pow2[N], MOD-2, MOD)
    print(ans%MOD)
solve()

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**8)

N = int(input())
AB = [tuple(map(int,input().split())) for i in range(N-1)]
MOD = 10**9+7
es = [[] for _ in range(N)]
for a,b in AB:
    a,b = a-1,b-1
    es[a].append(b)
    es[b].append(a)

cs = [1] * N
def dfs(v,p=-1):
    ret = 1
    for to in es[v]:
        if to==p: continue
        ret += dfs(to,v)
    cs[v] = ret
    return ret
dfs(0)
ans = 0
for i in range(N):
    if len(es[i]) == 1: continue
    ans += pow(2,N-1,MOD) - 1
    c = 0
    for to in es[i]:
        if cs[to] > cs[i]: continue
        c += cs[to]
        ans -= pow(2,cs[to],MOD) - 1
    ans -= pow(2,N-c-1,MOD) - 1

ans *= pow(pow(2,N,MOD), MOD-2, MOD)
print(ans%MOD)

Fixed submission:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**8)

def solve():
    N = int(input())
    AB = [tuple(map(int,input().split())) for i in range(N-1)]
    MOD = 10**9+7
    es = [[] for _ in range(N)]
    for a,b in AB:
        a,b = a-1,b-1
        es[a].append(b)
        es[b].append(a)

    cs = [1] * N
    def dfs(v,p=-1):
        ret = 1
        for to in es[v]:
            if to==p: continue
            ret += dfs(to,v)
        cs[v] = ret
        return ret
    dfs(0)

    pow2 = [1]
    for i in range(N):
        pow2.append((pow2[-1]*2) % MOD)

    ans = 0
    for i in range(N):
        if len(es[i]) == 1: continue
        ans += pow2[N-1] - 1
        c = 0
        for to in es[i]:
            if cs[to] > cs[i]: continue
            c += cs[to]
            ans -= pow2[cs[to]] - 1
        ans -= pow2[N-c-1] - 1

    ans *= pow(pow2[N], MOD-2, MOD)
    print(ans%MOD)
solve()

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**8)

N = int(input())
AB = [tuple(map(int,input().split())) for i in range(N-1)]
MOD = 10**9+7
es = [[] for _ in range(N)]
for a,b in AB:
    a,b = a-1,b-1
    es[a].append(b)
    es[b].append(a)

cs = [1] * N
def dfs(v,p=-1):
    ret = 1
    for to in es[v]:
        if to==p: continue
        ret += dfs(to,v)
    cs[v] = ret
    return ret
dfs(0)
ans = 0
for i in range(N):
    if len(es[i]) == 1: continue
    ans += pow(2,N-1,MOD) - 1
    c = 0
    for to in es[i]:
        if cs[to] > cs[i]: continue
        c += cs[to]
        ans -= pow(2,cs[to],MOD) - 1
    ans -= pow(2,N-c-1,MOD) - 1

ans *= pow(2,-N,MOD)
print(ans%MOD)

Fixed submission:
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**8)

def solve():
    N = int(input())
    AB = [tuple(map(int,input().split())) for i in range(N-1)]
    MOD = 10**9+7
    es = [[] for _ in range(N)]
    for a,b in AB:
        a,b = a-1,b-1
        es[a].append(b)
        es[b].append(a)

    cs = [1] * N
    def dfs(v,p=-1):
        ret = 1
        for to in es[v]:
            if to==p: continue
            ret += dfs(to,v)
        cs[v] = ret
        return ret
    dfs(0)

    pow2 = [1]
    for i in range(N):
        pow2.append((pow2[-1]*2) % MOD)

    ans = 0
    for i in range(N):
        if len(es[i]) == 1: continue
        ans += pow2[N-1] - 1
        c = 0
        for to in es[i]:
            if cs[to] > cs[i]: continue
            c += cs[to]
            ans -= pow2[cs[to]] - 1
        ans -= pow2[N-c-1] - 1

    ans *= pow(pow2[N], MOD-2, MOD)
    print(ans%MOD)
solve()