#ifdef DEBUG
#define _GLIBCXX_DEBUG
#endif
//#pragma GCC optimize("O3")
#include<bits/stdc++.h>
using namespace std;

#define pb push_back

typedef long long ll;
typedef long double ld;
int n, m;
const int maxN = 1e5 + 10;
ld p[maxN];
const int BUBEN = 40;
ld dp[2 * 134'000][BUBEN];
ld lazy[4 * maxN];
void merge(int v) {
    for (int k = 0; k < BUBEN; k++) {
        dp[v][k] = dp[2 * v][k] + dp[2 * v + 1][k];
    }
}
void build(int v, int tl, int tr) {
    lazy[v] = 0;
    if (tl == tr) {
        dp[v][0] = 1;
        for (int z = 1; z < BUBEN; z++) {
            dp[v][z] = dp[v][z - 1] * p[tl];
        }
        return;
    }
//    cout << " TUT " << v << " " << tl << " " << tr << endl;
    int tm = (tl + tr) / 2;
    build(2 * v, tl, tm);
    build(2 * v + 1, tm + 1, tr);
    merge(v);
}
ld ans = 0;
void apply(int v, ld k) {
    ld x = 1;
    lazy[v] += k;
    ld f = expl(k);
    for (int z = 0; z < BUBEN; z++) {
        dp[v][z] *= x;
        x *= f;
    }
}
void push(int v, int tl, int tr) {
    if (tl != tr) {
        apply(2 * v, lazy[v]);
        apply(2 * v + 1, lazy[v]);
    }
    lazy[v] = 0;
}
void go(int v, int tl, int tr, int l, int r) {
    if (tr < l || tl > r) return;
    if (l <= tl && tr <= r) {
        for (int k = 1; k < BUBEN; k++) ans += dp[v][k] / k;
        return;
    }
    push(v, tl, tr);
    int tm = (tl + tr) / 2;
    go(2 * v, tl, tm, l, r);
    go(2 * v + 1, tm + 1, tr, l, r);
}
void upd(int v, int tl, int tr, int l, int r, ld k) {
    if (tr < l || tl > r) return;
    if (l <= tl && tr <= r) {
        apply(v, k);
        return;
    }
    push(v, tl, tr);
    int tm = (tl + tr) / 2;
    upd(2 * v, tl, tm, l, r, k);
    upd(2 * v + 1, tm + 1, tr, l, r, k);
    merge(v);
}
void solve() {
    for (int i = 1; i <= n; i++) {
        cin >> p[i];
    }
    build(1, 1, n);
//    cout << m << " ??? " << endl;
    while (m--) {
        int tp, l, r;
        cin >> tp >> l >> r;
        if (tp == 0) {
            ans = 0;
            go(1, 1, n, l, r);
            cout << fixed << setprecision(25) << -ans << '\n';
        }
        else {
            ld k;
            cin >> k;
            k = logl(k);
            upd(1, 1, n, l, r, k);
        }
    }
}
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#ifdef DEBUG
    freopen("input.txt", "r", stdin);
#endif
    while (cin >> n >> m) {
        solve();
    }
    return 0;
}