Problem p02728 (python)

Fixed submission:
import sys
sys.setrecursionlimit(10 ** 7)

MOD = 10**9 + 7

def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u

def init_Graph(G):
    for _ in range(len(G)-1):
        a, b = map(int, input().split())
        a, b = a-1, b-1
        G[a].append(b)
        G[b].append(a)

def dfs(G, dp, t, perm, crr, pre):
    tmp = 1
    f = False
    for nxt in G[crr]:
        if nxt == pre:
            continue
        dfs(G, dp, t, perm, nxt, crr)
        t[crr] += t[nxt]
        tmp *= dp[nxt]
        f = True
    if f:
        dp[crr] = perm[t[crr]-1]
        for nxt in G[crr]:
            if nxt == pre:
                continue
            dp[crr] *= MOD_inv(perm[t[nxt]]) * dp[nxt]
            dp[crr] %= MOD
    else:
        dp[crr] = 1

def solve(G, dp, t, perm, crr, pre, mul):
    dp[crr] *= MOD_inv(perm[t[crr]-1]) * perm[len(G)-1] * mul
    dp[crr] %= MOD
    for nxt in G[crr]:
        if nxt == pre:
            continue
        crr_t = len(G)
        crr_t -= t[nxt]
        crr_dp = dp[crr]
        crr_dp *= perm[t[nxt]] * MOD_inv(perm[len(G)-1]) * perm[len(G)-t[nxt]-1] * MOD_inv(dp[nxt])
        crr_dp %= MOD
        tmp = MOD_inv(perm[crr_t]) * crr_dp % MOD
        solve(G, dp, t, perm, nxt, crr, tmp)

def main():
    n = int(input())
    G = [[] for _ in range(n)]
    init_Graph(G)
    t = [1]*n
    dp = [0]*n
    perm = [1]*(2 * 10**5 + 10)
    for i in range(2, 2 * 10**5 + 10):
        perm[i] = perm[i-1] * i % MOD
    dfs(G, dp, t, perm, 0, -1)
    solve(G, dp, t, perm, 0, -1, 1)
    for v in dp:
        print(v)

if __name__ == "__main__":
    main()

Buggy submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(10 ** 7)

MOD = 10**9 + 7
MOD_t_MAX = 2 * 10**5 + 10

fac  = [None] * MOD_t_MAX
finv = [None] * MOD_t_MAX
inv  = [None] * MOD_t_MAX
def MOD_COM_init():
    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1
    for i in range(2, MOD_t_MAX):
        fac[i] = fac[i - 1] * i % MOD
        inv[i] = MOD - inv[MOD%i] * (MOD // i) % MOD
        finv[i] = finv[i - 1] * inv[i] % MOD
def MOD_COM(n, k):
    if n < k:
        return 0
    if n < 0 or k < 0:
        return 0
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD
def MOD_inv(a):
    b = MOD
    u = 1
    v = 0
    while b > 0:
        t = a // b
        a -= t * b
        a, b = b, a
        u -= t * v
        u, v = v, u
    u = u % MOD
    if u < 0:
        u += MOD
    return u

def init_Graph(G):
    for _ in range(len(G)-1):
        a, b = map(int, input().split())
        a, b = a-1, b-1
        G[a].append(b)
        G[b].append(a)

def dfs(G, dp, t, perm, crr, pre):
    tmp = 1
    f = False
    for nxt in G[crr]:
        if nxt == pre:
            continue
        dfs(G, dp, t, perm, nxt, crr)
        t[crr] += t[nxt]
        tmp *= dp[nxt]
        f = True
    if f:
        dp[crr] = perm[t[crr]-1]
        for nxt in G[crr]:
            if nxt == pre:
                continue
            dp[crr] *= inv[perm[t[nxt]]] * dp[nxt]
            dp[crr] %= MOD
    else:
        dp[crr] = 1

def solve(G, dp, t, perm, crr, pre, mul):
    dp[crr] *= inv[perm[t[crr]-1]] * perm[len(G)-1] * mul
    dp[crr] %= MOD
    for nxt in G[crr]:
        if nxt == pre:
            continue
        crr_t = len(G)
        crr_t -= t[nxt]
        crr_dp = dp[crr]
        crr_dp *= perm[t[nxt]] * inv[perm[len(G)-1]] * perm[len(G)-t[nxt]-1] * inv[dp[nxt]]
        crr_dp %= MOD
        tmp = inv[perm[crr_t]] * crr_dp % MOD
        solve(G, dp, t, perm, nxt, crr, tmp)

def main():
    n = int(input())
    G = [[] for _ in range(n)]
    init_Graph(G)
    MOD_COM_init()
    t = [1]*n
    dp = [0]*n
    perm = [1]*(2 * 10**5 + 10)
    for i in range(2, 2 * 10**5 + 10):
        perm[i] = perm[i-1] * i % MOD
    dfs(G, dp, t, perm, 0, -1)
    solve(G, dp, t, perm, 0, -1, 1)
    for v in dp:
        print(v)

if __name__ == "__main__":
    main()