백준11505, 교재 73번

#include <iostream>
#include <vector>
#include <cmath>
using namespace std;

static vector<long> tree;
static int n, m, k,mod = 1000000007;
void tree_set(int a);
void change_val(int index, long val);
long gugan(int s, int e);
int main() {
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);

	cin >> n >> m >> k;
	int q = n;
	int l = 0;
	while (q != 0) {
		q = q / 2;
		l++;
	}
	int tree_size = int(pow(2, l+1));
	int left_index = pow(2, l);
	tree.resize(tree_size);
	fill(tree.begin(), tree.end(), 1);
	for (int i = left_index; i < n+left_index; i++) {
		cin >> tree[i];
	}
	tree_set(tree_size-1);
	for (int i = 0; i < m + k; i++) {
		long a, s, e;
		cin >> a >> s >> e;

		if (a == 1) {
			change_val(s + left_index - 1, e);
		}	
		else if (a == 2) {
			long start = s + left_index - 1;
			long end = e + left_index - 1;
			long result = gugan(start, end);
			cout<<result<<'\n';
		}
	}

}
long gugan(int s, int e) {
	long part_sum = 1;
	while (s <= e) {
		if (s % 2 == 1) {
			part_sum *= tree[s]%mod;
		}
		if (e % 2 == 0) {
			part_sum *= tree[e]%mod;
		}
		s = (s + 1) / 2;
		e = (e - 1) / 2;
	}
	return part_sum;
}
void change_val(int index, long val) {
	tree[index] = val;
	while (index > 1) {
		index = index / 2;
		tree[index] = tree[index*2]%mod*tree[index*2+1]%mod;
	}
}
void tree_set(int a) {
	while (a != 1) {
		tree[a / 2] *= tree[a]%mod;
		a--;
	}
}

위의 방법으로 코드를짜서 제출했더니 출력초과가 발생합니다. 왜 이런오류가 발생하는지 모르겠습니다..