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>
using namespace std;
#include<vector>
#include<functional>
template<typename T>
struct lazysegtree{
	function<T(T,T)>calcfn,lazycalcfn;
	function<T(T,T,unsigned int)>updatefn;
	int n;
	T defvalue,lazydefvalue;
	vector<T>dat,lazy;
	vector<bool>lazyflag;
	lazysegtree(int n_=0,T defvalue_=0,T lazydefvalue_=0,
		function<T(T,T)>calcfn_=[](T a,T b){return a+b;},
		function<T(T,T)>lazycalcfn_=[](T a,T b){return a+b;},
		function<T(T,T,unsigned int)>updatefn_=[](T a,T b,unsigned int width){return a+b*width;}
	):defvalue(defvalue_),lazydefvalue(lazydefvalue_),
		calcfn(calcfn_),lazycalcfn(lazycalcfn_),updatefn(updatefn_)
	{
		n=1;
		while(n<n_)n<<=1;
		dat.assign(2*n-1,defvalue);
		lazy.assign(2*n-1,lazydefvalue);
		lazyflag.assign(2*n-1,false);
	}
	void copy(vector<T>v)
	{
		for(int i=0;i<v.size();i++)dat[i+n-1]=v[i];
		for(int i=n-2;i>=0;i--)dat[i]=calcfn(dat[2*i+1],dat[2*i+2]);
	}
	void eval(int i,int l,int r)
	{
		if(lazyflag[i])
		{
			dat[i]=updatefn(dat[i],lazy[i],r-l);
			if(r-l>1)
			{
				lazy[2*i+1]=lazycalcfn(lazy[2*i+1],lazy[i]);
				lazy[2*i+2]=lazycalcfn(lazy[2*i+2],lazy[i]);
				lazyflag[2*i+1]=lazyflag[2*i+2]=true;
			}
			lazy[i]=lazydefvalue;
			lazyflag[i]=false;
		}
	}
	void update(int a,int b,T x,int k=0,int l=0,int r=-1)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return;
		else if(a<=l&&r<=b)
		{
			lazy[k]=lazycalcfn(lazy[k],x);
			lazyflag[k]=true;
			eval(k,l,r);
		}
		else
		{
			update(a,b,x,2*k+1,l,(l+r)/2);
			update(a,b,x,2*k+2,(l+r)/2,r);
			dat[k]=calcfn(dat[2*k+1],dat[2*k+2]);
		}
	}
	T query(int a,int b,int k=0,int l=0,int r=-1)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return defvalue;
		else if(a<=l&&r<=b)return dat[k];
		else return calcfn(
			query(a,b,2*k+1,l,(l+r)/2),
			query(a,b,2*k+2,(l+r)/2,r)
		);
	}
};
int main()
{
	int n,q;cin>>n>>q;
	lazysegtree<long long>S(n);
	for(int i=0;i<q;i++)
	{
		int c;cin>>c;
		if(c)
		{
			int s,t;cin>>s>>t;
			cout<<S.query(s-1,t)<<endl;
		}
		else
		{
			int s,t,x;cin>>s>>t>>x;
			S.update(s-1,t,x);
		}
	}
}