Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**9)

n, mod = map(int, input().split())
graph = [[] for _ in range(n)]
for _ in range(n - 1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)

ele_id = 1
# dp[v][i] = (頂点vから出るi番目の有向辺に関する部分木のDPの値)
# dp[v][i] = (c, m)
# c = 頂点vから出るi番目の有向辺に関する部分木の塗り方の数
# m = 頂点vから出るi番目の有向辺に関する部分木の頂点数
dp = [[ele_id] * len(graph[i]) for i in range(n)]
ans = [ele_id] * n

add_func = lambda x: x + 1
merge_func = lambda a, b: a * b % mod


def dfs1(v, v_p):
    dp_cum = ele_id
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dp[v][i] = dfs1(v_next, v)
        dp_cum = merge_func(dp_cum, dp[v][i])
    return add_func(dp_cum)


def dfs2(v, v_p, dp_vp):
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            dp[v][i] = dp_vp

    dp_l = [ele_id] * (len(graph[v]) + 1)
    dp_r = [ele_id] * (len(graph[v]) + 1)
    for i in range(len(graph[v])):
        dp_l[i + 1] = merge_func(dp_l[i], dp[v][i])
    for i in reversed(range(len(graph[v]))):
        dp_r[i] = merge_func(dp_r[i + 1], dp[v][i])

    ans[v] = add_func(dp_l[-1])

    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dfs2(v_next, v, add_func(merge_func(dp_l[i], dp_r[i + 1])))


dfs1(0, -1)
# print(*dp, sep='\n')
dfs2(0, -1, ele_id)
for ans_i in ans:
    print(ans_i - 1)


Fixed submission:
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n, mod = map(int, input().split())
graph = [[] for _ in range(n)]
for _ in range(n - 1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)

ele_id = 1
# dp[v][i] = (頂点vから出るi番目の有向辺に関する部分木のDPの値)
# dp[v][i] = (c, m)
# c = 頂点vから出るi番目の有向辺に関する部分木の塗り方の数
# m = 頂点vから出るi番目の有向辺に関する部分木の頂点数
dp = [[ele_id] * len(graph[i]) for i in range(n)]
ans = [ele_id] * n

add_func = lambda x: x + 1
merge_func = lambda a, b: a * b % mod


def dfs1(v, v_p):
    dp_cum = ele_id
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dp[v][i] = dfs1(v_next, v)
        dp_cum = merge_func(dp_cum, dp[v][i])
    return add_func(dp_cum)


def dfs2(v, v_p, dp_vp):
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            dp[v][i] = dp_vp

    dp_l = [ele_id] * (len(graph[v]) + 1)
    dp_r = [ele_id] * (len(graph[v]) + 1)
    for i in range(len(graph[v])):
        dp_l[i + 1] = merge_func(dp_l[i], dp[v][i])
    for i in reversed(range(len(graph[v]))):
        dp_r[i] = merge_func(dp_r[i + 1], dp[v][i])

    ans[v] = add_func(dp_l[-1])

    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dfs2(v_next, v, add_func(merge_func(dp_l[i], dp_r[i + 1])))


dfs1(0, -1)
# print(*dp, sep='\n')
dfs2(0, -1, ele_id)
for ans_i in ans:
    print(ans_i - 1)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**9)

n, mod = map(int, input().split())
graph = [[] for _ in range(n)]
for _ in range(n - 1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)

ele_id = 1
# dp[v][i] = (頂点vから出るi番目の有向辺に関する部分木のDPの値)
# dp[v][i] = (c, m)
# c = 頂点vから出るi番目の有向辺に関する部分木の塗り方の数
# m = 頂点vから出るi番目の有向辺に関する部分木の頂点数
dp = [[ele_id] * len(graph[i]) for i in range(n)]
ans = [ele_id] * n

add_func = lambda x: x + 1
merge_func = lambda a, b: a * b % mod


def dfs1(v, v_p):
    dp_cum = ele_id
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dp[v][i] = dfs1(v_next, v)
        dp_cum = merge_func(dp_cum, dp[v][i])
    return add_func(dp_cum)


def dfs2(v, v_p, dp_vp):
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            dp[v][i] = dp_vp

    dp_l = [ele_id] * (len(graph[v]) + 1)
    dp_r = [ele_id] * (len(graph[v]) + 1)
    for i in range(len(graph[v])):
        dp_l[i + 1] = merge_func(dp_l[i], dp[v][i])
    for i in reversed(range(len(graph[v]))):
        dp_r[i] = merge_func(dp_r[i + 1], dp[v][i])

    ans[v] = add_func(dp_l[-1])

    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dfs2(v_next, v, add_func(merge_func(dp_l[i], dp_r[i + 1])))


dfs1(0, -1)
# print(*dp, sep='\n')
dfs2(0, -1, ele_id)
for ans_i in ans:
    print(ans_i - 1)


Fixed submission:
import sys
sys.setrecursionlimit(10**9)
input = sys.stdin.readline

n, mod = map(int, input().split())
graph = [[] for _ in range(n)]
for _ in range(n - 1):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    graph[a].append(b)
    graph[b].append(a)

ele_id = 1
# dp[v][i] = (頂点vから出るi番目の有向辺に関する部分木のDPの値)
# dp[v][i] = (c, m)
# c = 頂点vから出るi番目の有向辺に関する部分木の塗り方の数
# m = 頂点vから出るi番目の有向辺に関する部分木の頂点数
dp = [[ele_id] * len(graph[i]) for i in range(n)]
ans = [ele_id] * n

add_func = lambda x: x + 1
merge_func = lambda a, b: a * b % mod


def dfs1(v, v_p):
    dp_cum = ele_id
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dp[v][i] = dfs1(v_next, v)
        dp_cum = merge_func(dp_cum, dp[v][i])
    return add_func(dp_cum)


def dfs2(v, v_p, dp_vp):
    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            dp[v][i] = dp_vp

    dp_l = [ele_id] * (len(graph[v]) + 1)
    dp_r = [ele_id] * (len(graph[v]) + 1)
    for i in range(len(graph[v])):
        dp_l[i + 1] = merge_func(dp_l[i], dp[v][i])
    for i in reversed(range(len(graph[v]))):
        dp_r[i] = merge_func(dp_r[i + 1], dp[v][i])

    ans[v] = add_func(dp_l[-1])

    for i, v_next in enumerate(graph[v]):
        if v_next == v_p:
            continue
        dfs2(v_next, v, add_func(merge_func(dp_l[i], dp_r[i + 1])))


dfs1(0, -1)
# print(*dp, sep='\n')
dfs2(0, -1, ele_id)
for ans_i in ans:
    print(ans_i - 1)