#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;
const int BLOCK = 600;
ld F[maxN / BLOCK + 2][BUBEN];
int from[maxN / BLOCK + 2], to[maxN / BLOCK + 2];
ld coef[maxN / BLOCK + 2];
void solve() {
    for (int i = 0; i <= n / BLOCK; i++) {
        coef[i] = 1;
        for (int j = 0; j < BUBEN; j++) {
            F[i][j] = 0;
        }
    }
    for (int i = 0; i < n; i++) {
        cin >> p[i];
        int id = i / BLOCK;
        ld cur = 1;
        for (int j = 0; j < BUBEN; j++) {
            F[id][j] += cur;
            cur *= p[i];
        }
    }
    for (int i = 0; i < n; i += BLOCK) {
        from[i / BLOCK] = i;
        to[i / BLOCK] = min(n, i + BLOCK);
    }
    auto apply = [&](int bl) {
        for (int k = 0; k < BUBEN; k++) {
            F[bl][k] = 0;
        }
        assert(coef[bl] > 1e-7 && coef[bl] < 1e4);
        for (int j = from[bl]; j < to[bl]; j++) {
            p[j] *= coef[bl];
            ld cur = 1;
            for (int k = 0; k < BUBEN; k++) {
                F[bl][k] += cur;
                cur *= p[j];
            }
        }
        coef[bl] = 1;
    };
    while (m--) {
        if (m % 500 == 0) {
            for (int z = 0; z < n; z += BLOCK) {
                apply(z / BLOCK);
            }
        }
        int tp, l, r;
        cin >> tp >> l >> r;
        l--;
        r--;
        if (tp == 0) {
            int bl = l / BLOCK;
            int br = r / BLOCK;
            ld ans = 0;
            if (bl == br) {
                apply(bl);
                for (int j = l; j <= r; j++) {
                    ans += logl(1 - p[j]);
                }
            }
            else {
                apply(bl);
                apply(br);
                for (int j = bl + 1; j < br; j++) {
                    ld cur = 1;
                    for (int k = 1; k < BUBEN; k++) {
                        cur *= coef[j];
                        ans += (F[j][k] * cur) / k;
                    }
                }
                ans *= -1;
                for (int j = l; j < to[bl]; j++) ans += logl(1 - p[j]);
                for (int j = from[br]; j <= r; j++) ans += logl(1 - p[j]);
            }
            cout << fixed << setprecision(12) << ans << '\n';
        }
        else {
            int bl = l / BLOCK;
            int br = r / BLOCK;
            ld k;
            cin >> k;
            if (bl == br) {
                for (int j = l; j <= r; j++) {
                    p[j] *= k;
                }
                apply(bl);
            }
            else {
                for (int j = l; j < to[bl]; j++) p[j] *= k;
                apply(bl);
                for (int j = from[br]; j <= r; j++) p[j] *= k;
                apply(br);
                for (int j = bl + 1; j < br; j++) {
                    coef[j] *= 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;
}