Problem:
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Foehn Phenomena

In the Kingdom of IOI, the wind always blows from sea to land. There are $N + 1$ spots numbered from $0$ to $N$. The wind from Spot $0$ to Spot $N$ in order. Mr. JOI has a house at Spot $N$. The altitude of Spot $0$ is $A_0 = 0$, and the altitude of Spot $i$ ($1 \leq i \leq N$) is $A_i$.

The wind blows on the surface of the ground. The temperature of the wind changes according to the change of the altitude. The temperature of the wind at Spot $0$, which is closest to the sea, is $0$ degree. For each $i$ ($0 \leq i \leq N - 1$), the change of the temperature of the wind from Spot $i$ to Spot $i + 1$ depends only on the values of $A_i$ and $A_{i+1}$ in the following way:

If $A_i < A_{i+1}$, the temperature of the wind decreases by $S$ degrees per altitude.

If $A_i \geq A_{i+1}$, the temperature of the wind increases by $T$ degrees per altitude.

The tectonic movement is active in the land of the Kingdom of IOI. You have the data of tectonic movements for $Q$ days. In the $j$-th ($1 \leq j \leq Q$) day, the change of the altitude of Spot $k$ for $L_j \leq k \leq R_j$ ($1 \leq L_j \leq R_j \leq N$) is described by $X_j$. If $X_j$ is not negative, the altitude increases by $X_j$. If $X_j$ is negative, the altitude decreases by $|X_j|$.

Your task is to calculate the temperature of the wind at the house of Mr. JOI after each tectonic movement.

Task

Given the data of tectonic movements, write a program which calculates, for each $j$ ($1 \leq j \leq Q$), the temperature of the wind at the house of Mr. JOI after the tectonic movement on the $j$-th day.

Input

Read the following data from the standard input.

The first line of input contains four space separated integers $N$, $Q$, $S$, $T$. This means there is a house of Mr. JOI at Spot $N$, there are $Q$ tectonic movements, the temperature of the wind decreases by $S$ degrees per altitude if the altitude increases, and the temperature of the wind increases by $T$ degrees per altitude if the altitude decreases.

The $i$-th line ($1 \leq i \leq N +1$) of the following $N +1$ lines contains an integer $A_{i-1}$, which is the initial altitude at Spot ($i - 1$) before tectonic movements.

The $j$-th line ($1 \leq j \leq Q$) of the following $Q$ lines contains three space separated integers $L_j$, $R_j$, $X_j$. This means, for the tectonic movement on the $j$-th day, the change of the altitude at the spots from $L_j$ to $R_j$ is described by $X_j$.

Output

Write $Q$ lines to the standard output. The $j$-th line ($1 \leq j \leq Q$) of output contains the temperature of the wind
at the house of Mr. JOI after the tectonic movement on the $j$-th day.

Constraints

All input data satisfy the following conditions.

$1 \leq N \leq 200 000．$

$1 \leq Q \leq 200 000．$

$1 \leq S \leq 1 000 000．$

$1 \leq T \leq 1 000 000．$

$A_0 = 0．$

$-1 000 000 \leq A_i \leq 1 000 000 (1 \leq i \leq N)．$

$1 \leq L_j \leq R_j \leq N (1 \leq j \leq Q)．$

$ -1 000 000 \leq X_j \leq 1 000 000 (1 \leq j \leq Q)．$

Sample Input and Output

Sample Input 1

3 5 1 2
0
4
1
8
1 2 2
1 1 -2
2 3 5
1 2 -1
1 3 5

Sample Output 1

-5
-7
-13
-13
-18

Initially, the altitudes of the Spot 0, 1, 2, 3 are 0, 4, 1, 8, respectively. After the tectonic movement on the first day, the altitudes become 0, 6, 3, 8, respectively. At that moment, the temperatures of the wind are 0, -6, 0, -5,respectively.

Sample Input 2

2 2 5 5
0
6
-1
1 1 4
1 2 8

Sample Output 2

5
-35

Sample Input 3

7 8 8 13
0
4
-9
4
-2
3
10
-9
1 4 8
3 5 -2
3 3 9
1 7 4
3 5 -1
5 6 3
4 4 9
6 7 -10

Sample output 3

277
277
322
290
290
290
290
370

The 16th Japanese Olympiad in Informatics (JOI 2016/2017)
Final Round

Solution in C (judge verdict: Accepted)

#include <stdio.h>
#include <inttypes.h>

#define MAX (1 << 18) /* 262144 */
#define INF INT64_C(99999999999999999)

int64_t ki[MAX * 2 - 1], ki_all[MAX * 2 - 1];

void ki_add_i(int idx, int qs, int qe, int qdelta, int ss, int se) {
	if (qe <= ss || se <= qs) { /* query ga segument kara kanzen ni hazurete iru */
		/* NOP */
	} else if (qs <= ss && se <= qe) { /* segment ga query ni kanzen ni fukumareru */
		ki_all[idx] += qdelta;
	} else {
		int sm = ss + (se - ss) / 2;
		int lidx = idx * 2 + 1, ridx = idx * 2 + 2;
		int64_t l, r;
		ki_all[lidx] += ki_all[idx];
		ki_all[ridx] += ki_all[idx];
		ki_all[idx] = 0;
		ki_add_i(lidx, qs, qe, qdelta, ss, sm);
		ki_add_i(ridx, qs, qe, qdelta, sm ,se);
		l = ki[lidx] + ki_all[lidx];
		r = ki[ridx] + ki_all[ridx];
		ki[idx] = l >= r ? l : r;
	}
}

void ki_add(int s, int e, int delta) {
	ki_add_i(0, s, e, delta, 0, MAX);
}

int64_t ki_get_i(int idx, int qs, int qe, int ss, int se) {
	if (qe <= ss || se <= qs) { /* query ga segument kara kanzen ni hazurete iru */
		return -INF;
	} else if (qs <= ss && se <= qe) { /* segment ga query ni kanzen ni fukumareru */
		return ki[idx] + ki_all[idx];
	} else {
		int sm = ss + (se - ss) / 2;
		int lidx = idx * 2 + 1, ridx = idx * 2 + 2;
		int64_t l, r;
		l = ki_get_i(lidx, qs, qe, ss, sm);
		r = ki_get_i(ridx, qs, qe, sm ,se);
		return (l >= r ? l : r) + ki_all[idx];
	}
}

int64_t ki_get(int idx) {
	return ki_get_i(0, idx, idx + 1, 0, MAX);
}

int N, Q, S, T;
int A[222222];
int L[222222], R[222222], X[222222];

int64_t getDelta(int64_t from, int64_t to) {
	if (from >= to) {
		return (int64_t)T * (from - to);
	} else {
		return -(int64_t)S * (to - from);
	}
}

int main(void) {
	int i;
	int64_t kaze = 0;
	if (scanf("%d%d%d%d", &N, &Q, &S, &T) != 4) return 1;
	for (i = 0; i <= N; i++) {
		if (scanf("%d", &A[i]) != 1) return 1;
	}
	for (i = 0; i < Q; i++) {
		if (scanf("%d%d%d", &L[i], &R[i], &X[i]) != 3) return 1;
	}
	ki_add(0, 1, A[0]);
	for (i = 1; i <= N; i++) {
		ki_add(i, i + 1, A[i]);
		kaze += getDelta(A[i - 1], A[i]);
	}
	for (i = 0; i < Q; i++) {
		int64_t prev = ki_get(L[i] - 1);
		int64_t next = ki_get(R[i] + 1);
		int64_t asumi = ki_get(L[i]);
		int64_t iguti = ki_get(R[i]);
		ki_add(L[i], R[i] + 1, X[i]);
		kaze -= getDelta(prev, asumi);
		kaze += getDelta(prev, ki_get(L[i]));
		if (R[i] < N) {
			kaze -= getDelta(iguti, next);
			kaze += getDelta(ki_get(R[i]), next);
		}
		printf("%" PRId64 "\n", kaze);
	}
	return 0;
}