#include "towers.h"
#include<bits/stdc++.h>
#define all(v) v.begin(), v.end()
using namespace std;
const int N = 1e5 + 10, S = 1e5 * 20 * 2;
int h[N], lg[N], mx[20][N], mn[20][N], L[N], R[N];
int n;
vector<int> rrh, pos[2 * N];
int idx(int x) {
return upper_bound(all(rrh), x) - rrh.begin();
}
struct ITSUM {
struct node {
int left, right, val;
node () {
left = right = val = 0;
}
} T[S];
int cnt;
int it[2 * N];
void pass (int x, int y) {
T[it[x] = ++cnt] = T[it[y]];
}
void up(int s, int l, int r, int pos, int val) {
if (l == r) {
T[s].val += val;
return;
}
int mid = l + r >> 1;
if (pos <= mid) {
T[++cnt] = T[T[s].left];
T[s].left = cnt;
up(T[s].left, l, mid, pos, val);
}
else {
T[++cnt] = T[T[s].right];
T[s].right = cnt;
up(T[s].right, mid + 1, r, pos, val);
}
T[s].val = T[T[s].left].val + T[T[s].right].val;
}
int get(int s, int l, int r, int from, int to) {
if (l > to || r < from || s == 0) return 0;
if (from <= l && r <= to) return T[s].val;
int mid = l + r >> 1;
return get(T[s].left, l, mid, from, to) + get(T[s].right, mid + 1, r, from, to);
}
} itsum;
struct ITMAX {
struct node {
int left, right, val;
node () {
left = right = 0;
val = -1e9;
}
} T[S];
int cnt;
int it[2 * N];
void pass (int x, int y) {
T[it[x] = ++cnt] = T[it[y]];
}
void up(int s, int l, int r, int from , int to, int val) {
if (l > to || r < from) return;
if (from <= l && r <= to) {
T[s].val = max(T[s].val, val);
return;
}
int mid = l + r >> 1;
T[++cnt] = T[T[s].left];
T[s].left = cnt;
T[++cnt] = T[T[s].right];
T[s].right = cnt;
up(T[s].left, l, mid, from, to, val);
up(T[s].right, mid + 1, r, from, to, val);
}
int get(int s, int l, int r, int pos) {
// cerr << s << " " << l << " " << r << endl;
if (l == r || !s) return T[s].val;
int mid = l + r >> 1;
// cout << T[s].left << e
// exit(0);
if (pos <= mid) return max(T[s].val, get(T[s].left, l, mid, pos));
return max(T[s].val, get(T[s].right, mid + 1, r, pos));
}
} itmax0, itmax1;
int getmax(int l, int r) {
if (l > r) return -1e9;
int k = lg[r - l + 1];
return max(mx[k][l], mx[k][r - (1 << k) + 1]);
}
int best (int x, int y) {
return h[x] < h[y] ? x : y;
}
int getmin(int l, int r) {
if (l > r) return -1e9;
int k = lg[r - l + 1];
return best(mn[k][l], mn[k][r - (1 << k) + 1]);
}
priority_queue<int> Q[N];
bool alive[N];
void init(int N, std::vector<int> H) {
n = N;
for(int i = 0; i < n; i++) h[i] = H[i];
stack<int> st;
for(int i = 0; i < n; i++) {
while (!st.empty() && h[st.top()] >= h[i]) st.pop();
L[i] = st.empty() ? -1 : st.top();
st.push(i);
}
while (!st.empty()) st.pop();
for(int i = n - 1; i >= 0; i--) {
while (!st.empty() && h[st.top()] >= h[i]) st.pop();
R[i] = st.empty() ? n : st.top();
st.push(i);
}
for(int i = 0; i < n; i++) mx[0][i] = h[i], mn[0][i] = i;
for(int i = 2; i <= n; i++) lg[i] = lg[i / 2] + 1;
for(int j = 1; j <= lg[n]; j++) for(int i = 0; i + (1 << j) - 1 < n; i++) {
mx[j][i] = max(mx[j - 1][i], mx[j - 1][i + (1 << j - 1)]);
mn[j][i] = best(mn[j - 1][i], mn[j - 1][i + (1 << j - 1)]);
}
for(int i = 0; i < n; i++) {
int tmp = min(getmax(L[i] + 1, i - 1), getmax(i + 1, R[i] - 1)) - h[i];
rrh.push_back(getmax(L[i] + 1, i - 1) - h[i]);
rrh.push_back(getmax(i + 1, R[i] - 1) - h[i]);
}
sort(all(rrh));
rrh.resize(unique(all(rrh)) - rrh.begin());
int m = rrh.size();
for(int i = 0; i < n; i++) {
int tmp = min(getmax(L[i] + 1, i - 1), getmax(i + 1, R[i] - 1)) - h[i];
// cout << getmax(L[i] + 1, i - 1) << " " << getmax(i + 1, R[i] - 1) << " " << i << endl;
pos[idx(tmp)].push_back(i);
}
for(int val = m; val >= 1; val--) {
itsum.pass(val, val + 1);
for(int &i : pos[val]) {
itsum.up(itsum.it[val], 0, n - 1, i, 1);
} pos[val].clear();
}
for(int i = 0; i < n; i++) {
int tmp = getmax(i + 1, R[i] - 1) - h[i];
// cout << idx(tmp) << endl;
pos[idx(tmp)].push_back(i);
}
for(int val = m; val >= 1; val--) {
itmax0.pass(val, val + 1);
for(int &i : pos[val]) {
itmax0.up(itmax0.it[val], 0, n - 1, L[i] + 1, i, -i);
// cout << itmax0.get(itmax0.it[val], 0, n - 1, i) << endl;
} pos[val].clear();
}
for(int i = 0; i < n; i++) {
int tmp = getmax(L[i] + 1, i - 1) - h[i];
pos[idx(tmp)].push_back(i);
}
for(int val = m; val >= 1; val--) {
itmax1.pass(val, val + 1);
for(int &i : pos[val]) {
itmax1.up(itmax1.it[val], 0, n - 1, i, R[i] - 1, i);
}
}
}
int max_towers(int l, int r, int d) {
int tmp = idx(d - 1) + 1;
int ans = itsum.get(itsum.it[tmp], 0, n - 1, l, r);
// cout << ans << endl;
int left = -itmax0.get(itmax0.it[tmp], 0, n - 1, l);
int right = itmax1.get(itmax1.it[tmp], 0, n - 1, r);
int smallest = getmin(l, r);
// cout << smallest << " " << left << " " << right << endl;
if (left >= l && left <= r && left != smallest && getmax(L[left] + 1, left - 1) - d < h[left]) {
ans++;
}
// exit(0);
if (right >= l && right <= r && right != smallest && getmax(right + 1, R[right] - 1) - d < h[right]) {
ans++;
}
if (getmax(L[smallest] + 1, smallest - 1) - d < h[smallest] || getmax(smallest + 1, R[smallest] - 1) - d < h[smallest]) ans++;
return ans;
}
#ifdef ngu
int main() {
freopen ("task.inp", "r", stdin);
freopen ("task.out", "w", stdout);
int N, Q;
assert(2 == scanf("%d %d", &N, &Q));
std::vector<int> H(N);
for (int i = 0; i < N; ++i) {
assert(1 == scanf("%d", &H[i]));
}
init(N, H);
for (int i = 0; i < Q; ++i) {
int L, R, D;
assert(3 == scanf("%d %d %d", &L, &R, &D));
printf("%d\n", max_towers(L, R, D));
}
return 0;
}
#endif // ngu
