Problem: Write a program which manipulates a sequence A = {a1, a2, . . . , an} with the following operations:

* add(s, t, x): add x to as, as+1, ..., at.
* getSum(s, t): report the sum of as, as+1, ..., at.



Note that the initial values of ai (i = 1, 2, . . . , n) are 0.

Constraints

* 1 ≤ n ≤ 100000
* 1 ≤ q ≤ 100000
* 1 ≤ s ≤ t ≤ n
* 0 ≤ x < 1000

Input


n q
query1
query2
:
queryq


In the first line, n (the number of elements in A) and q (the number of queries) are given. Then, ith query queryi is given in the following format:


0 s t x


or


1 s t


The first digit represents the type of the query. '0' denotes add(s, t, x) and '1' denotes getSum(s, t).

Output

For each getSum operation, print the sum;

Examples

Input

3 5
0 1 2 1
0 2 3 2
0 3 3 3
1 1 2
1 2 3


Output

4
8


Input

4 3
1 1 4
0 1 4 1
1 1 4


Output

0
4

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <algorithm>
#include <math.h>
#include <numeric>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <time.h>
#include <list>

using namespace std;
typedef long long ll;
#define rep(i,n) for(int i=0;i<(n);++i)
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define reps(x,c) for(auto x:c)
#define all(x) begin(x), end(x)
#define pb(a) emplace_back(a) 
#define mp(a,b) make_pair((a),(b))
#define pl pair<ll,ll>
#define INF 2147483647
#define MOD 1000000007
#define fi first
#define se second
#define dbg(x) cout << #x"="<< (x) << endl
#define dbgv(x) cout<<#x<<endl;reps(y,x){cout<<y<<" ";}cout<<endl

ll N;
vector<ll> node,lazy;
ll IDEN=0;
 
ll op(ll x,ll y){
	return x+y;
}
 
void seg_init(vector<ll> v){
	int sz=v.size();
	N=1;while(N<sz)N*=2;
	node.resize(2*N-1,IDEN);
	lazy.resize(2*N-1, IDEN);
	rep(i,sz)node[i+N-1]=v[i];
	for(int i=N-2; i>=0; i--) node[i]=op(node[2*i+1],node[2*i+2]);
}

void eval(ll k, ll l, ll r) {
  if(lazy[k] != 0) {
      node[k] += lazy[k];
      if(r - l > 1) {
          lazy[2*k+1] += lazy[k] / 2;
          lazy[2*k+2] += lazy[k] / 2;
      }
      lazy[k] = 0;
  }
}

void update(ll a, ll b,ll val,ll k=0,ll l=0, ll r=-1){
	if(r < 0) r = N;
	eval(k, l, r);
	if(b<=l || r<=a) return;
	if(a<=l && r<=b){
		lazy[k]+=(r-l)*val;
		eval(k,l,r);
	}else{
		update(a,b,val,2*k+1,l,(l+r)/2);
		update(a,b,val,2*k+2,(l+r)/2,r);
		node[k]=op(node[2*k+1],node[2*k+2]);
	}
}

ll query(ll a,ll b, ll k=0, ll l=0, ll r=-1){
	if(r<0) r=N;
	eval(k,l,r);
	if(b <= l || r <= a) return IDEN;
  if(a <= l && r <= b) return node[k];
  ll vl = query(a, b, 2*k+1, l, (l+r)/2);
  ll vr = query(a, b, 2*k+2, (l+r)/2, r);
  return op(vl,vr);
}
int main(){
	ll n,q;cin>>n>>q;
	seg_init(vector<ll>(n,IDEN));
	bool flg;
	ll s,t,x;
	rep(i,q){
		cin>>flg>>s>>t;
	  if(flg){
	  	cout<<query(s-1,t)<<endl;
	  }else{
	  	cin>>x;
	  	update(s-1,t,x);
	  }
	}
}