1535_E. Gold Transfer
You are given a rooted tree. Each vertex contains a_i tons of gold, which costs c_i per one ton. Initially, the tree consists only a root numbered 0 with a_0 tons of gold and price c_0 per ton.

There are q queries. Each query has one of two types: 

  1. Add vertex i (where i is an index of query) as a son to some vertex p_i; vertex i will have a_i tons of gold with c_i per ton. It's guaranteed that c_i > c_{p_i}. 
  2. For a given vertex v_i consider the simple path from v_i to the root. We need to purchase w_i tons of gold from vertices on this path, spending the minimum amount of money. If there isn't enough gold on the path, we buy all we can. 



If we buy x tons of gold in some vertex v the remaining amount of gold in it decreases by x (of course, we can't buy more gold that vertex has at the moment). For each query of the second type, calculate the resulting amount of gold we bought and the amount of money we should spend.

Note that you should solve the problem in online mode. It means that you can't read the whole input at once. You can read each query only after writing the answer for the last query, so don't forget to flush output after printing answers. You can use functions like fflush(stdout) in C++ and BufferedWriter.flush in Java or similar after each writing in your program. In standard (if you don't tweak I/O), endl flushes cout in C++ and System.out.println in Java (or println in Kotlin) makes automatic flush as well. 

Input

The first line contains three integers q, a_0 and c_0 (1 ≤ q ≤ 3 ⋅ 10^5; 1 ≤ a_0, c_0 < 10^6) — the number of queries, the amount of gold in the root and its price.

Next q lines contain descriptions of queries; The i-th query has one of two types: 

  * "1 p_i a_i c_i" (0 ≤ p_i < i; 1 ≤ a_i, c_i < 10^6): add vertex i as a son to vertex p_i. The vertex i will have a_i tons of gold with price c_i per one ton. It's guaranteed that p_i exists and c_i > c_{p_i}.
  * "2 v_i w_i" (0 ≤ v_i < i; 1 ≤ w_i < 10^6): buy w_i tons of gold from vertices on path from v_i to 0 spending the minimum amount of money. If there isn't enough gold, we buy as much as we can. It's guaranteed that vertex v_i exist. 



It's guaranteed that there is at least one query of the second type.

Output

For each query of the second type, print the resulting amount of gold we bought and the minimum amount of money we should spend.

Example

Input


5 5 2
2 0 2
1 0 3 4
2 2 4
1 0 1 3
2 4 2


Output


2 4
4 10
1 3

Note

Explanation of the sample:

At the first query, the tree consist of root, so we purchase 2 tons of gold and pay 2 ⋅ 2 = 4. 3 tons remain in the root.

At the second query, we add vertex 2 as a son of vertex 0. Vertex 2 now has 3 tons of gold with price 4 per one ton.

At the third query, a path from 2 to 0 consists of only vertices 0 and 2 and since c_0 < c_2 we buy 3 remaining tons of gold in vertex 0 and 1 ton in vertex 2. So we bought 3 + 1 = 4 tons and paid 3 ⋅ 2 + 1 ⋅ 4 = 10. Now, in vertex 0 no gold left and 2 tons of gold remain in vertex 2.

At the fourth query, we add vertex 4 as a son of vertex 0. Vertex 4 now has 1 ton of gold with price 3.

At the fifth query, a path from 4 to 0 consists of only vertices 0 and 4. But since no gold left in vertex 0 and only 1 ton is in vertex 4, we buy 1 ton of gold in vertex 4 and spend 1 ⋅ 3 = 3. Now, in vertex 4 no gold left.
```python
import os
import sys

input = sys.stdin.buffer.readline


def main():
    (Q, A0, C0) = [int(x) for x in input().split()]

    N = Q + 2

    A = [0] * N
    C = [0] * N
    P = [0] * N
    pref = [0] * N  # pref[u] is sum of A from root to u (inclusive, immutable)
    anc = [None for i in range(N)]  # anc[u][k] is (2**k)-th ancestor of u
    anc[-1] = [-1] * 20

    root = 0
    A[root] = A0
    C[root] = C0
    P[root] = -1
    pref[root] = A0
    anc[root] = [-1] * 20

    def buildJumps(u, parent):
        jumps = [0] * 20
        jumps[0] = parent
        for i in range(1, 20):
            jumps[i] = anc[jumps[i - 1]][i - 1]
        anc[u] = jumps

    def getAncestor(u, k):
        # Binary lifting, k-th ancestor of u
        for i in reversed(range(20)):
            if k & (1 << i):
                u = anc[u][i]
        return u

    def getLast(u, f):
        # Returns highest node on the path from u to root where f(node) is true.
        # Assumes f is monotonic and goes from true to false. If all false, returns u.
        for i in reversed(range(20)):
            if f(anc[u][i]):
                u = anc[u][i]
        return u

    for i in range(1, Q + 1):
        query = [int(x) for x in input().split()]
        if query[0] == 1:
            _, p, A[i], C[i] = query
            P[i] = p
            pref[i] = pref[p] + A[i]
            buildJumps(i, p)
        else:
            assert query[0] == 2
            _, v, want = query

            gold = 0
            spend = 0
            if False:
                if A[v] != 0:
                    hi = getLast(v, lambda node: A[node])
                    target = want + (pref[hi] - A[hi])
                    lo = getLast(v, lambda node: pref[node] >= target)

                    path = [lo]
                    while path[-1] != hi:
                        path.append(P[path[-1]])
                    for u in reversed(path):
                        take = min(want, A[u])
                        A[u] -= take
                        gold += take
                        spend += C[u] * take
                        want -= take

            else:
                while A[v] != 0 and want:
                    u = getLast(v, lambda node: A[node] != 0)
                    take = min(want, A[u])
                    A[u] -= take
                    gold += take
                    spend += C[u] * take
                    want -= take

            os.write(1, b"%d %d\n" % (gold, spend))


if __name__ == "__main__":
    main()

```