#include <bits/stdc++.h>

constexpr int MAXN = 1e5 + 19;
constexpr int MAX_LEN = 24;

struct Node {
    int n_line[MAX_LEN], last[MAX_LEN];
    friend Node operator*(const Node &lhs, const Node &rhs) {
        Node res;
        for (int i = 0; i < MAX_LEN; ++i) {
            int last = lhs.last[i];
            res.n_line[i] = lhs.n_line[i] + rhs.n_line[last] - 1;
            res.last[i] = rhs.last[last];
        }
        return res;
    }
    static Node from_int(int x) {
        Node res;
        for (int i = 0; i < MAX_LEN; ++i) {
            res.n_line[i] = (i + x) / MAX_LEN + 1;
            res.last[i] = (i + x) % MAX_LEN;
        }
        return res;
    }
} tr[MAXN << 2];

void modify(int node, int L, int R, int x, const Node &val) {
    if (L == R) {
        tr[node] = val;
        return;
    }
    int mid = (L + R) / 2;
    if (x <= mid) {
        modify(node << 1, L, mid, x, val);
    } else {
        modify(node << 1 | 1, mid + 1, R, x, val);
    }
    tr[node] = tr[node << 1] * tr[node << 1 | 1];
}

Node query(int node, int L, int R, int l, int r) {
    if (l <= L && R <= r) {
        return tr[node];
    }
    int mid = (L + R) / 2;
    if (r <= mid) {
        return query(node << 1, L, mid, l, r);
    } else if (l > mid) {
        return query(node << 1 | 1, mid + 1, R, l, r);
    } else {
        return query(node << 1, L, mid, l, r) * query(node << 1 | 1, mid + 1, R, l, r);
    }
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n, m;
    std::cin >> n >> m;

    std::vector<int> a(n + 1);
    for (int i = 1; i <= n; ++i) {
        std::cin >> a[i];
        modify(1, 1, n, i, Node::from_int(a[i]));
    }

    while (m--) {
        int op;
        std::cin >> op;
        if (op == 1) {
            int x, c;
            std::cin >> x >> c;
            modify(1, 1, n, x, Node::from_int(c));
        } else {
            int l, r;
            std::cin >> l >> r;
            auto res = query(1, 1, n, l, r);
            std::cout << res.n_line[0] - 1 + bool(res.last[0]) << '\n';
        }
    }
}