Given a sequence, you need to deal with the following two types of queries.

"C a B c" means that all values in [a, b] intervals are increased by C (-10000 < C < 10000).

"Q a b" asks the sum of all values in the [a, b] interval.

Input

The first line contains two integers N,Q. 1 < N,Q < 100000.

The second line contains n integers, representing the initial sequence A (-1000000000 < Ai < 1000000000).

Next, line Q asks in the form of a title description.

Output

For each Q-start question, you need to output the corresponding answers, one line for each answer.

Sample Input

10 5
1 2 3 4 5 6 7 8 9 10
Q 4 4
Q 1 10
Q 2 4
C 3 6 3
Q 2 4

Sample Output

4
55
9
15

Template problem

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
#define eps 0.00000001
using namespace std;
int q[400000];
struct point
{
    int l,r;
    long long nsum;
    long long add;
}node[400000];
void Build(int P,int L,int R)
{
    node[P].l=L;
    node[P].r=R;
    node[P].add=0;
    if(L==R)
    {
        node[P].nsum=q[L];
        return ;
    }
    int mid=L+((R-L)>>1);
    Build(P<<1,L,mid);
    Build(P<<1|1,mid+1,R);
    node[P].nsum=node[P<<1].nsum+node[P<<1|1].nsum;
}
void Add(int P,int L,int R,long long c)
{
    if(node[P].l==L&&node[P].r==R)
    {
        node[P].add+=c;
        return ;
    }
    node[P].nsum+=c*(R-L+1);
    int mid=(node[P].l+node[P].r)>>1;
    if(R<=mid) Add(P<<1,L,R,c);
    else if(L>mid) Add(P<<1|1,L,R,c);
    else
    {
        Add(P<<1,L,mid,c);
        Add(P<<1|1,mid+1,R,c);
    }
}
long long Query(int P,int L,int R)
{
    if(node[P].l==L&&node[P].r==R)
    {
        return node[P].nsum+(R-L+1)*node[P].add;
    }
    node[P].nsum+=(node[P].r-node[P].l+1)*node[P].add;
    int mid=(node[P].l+node[P].r)>>1;
    Add(P<<1,node[P].l,mid,node[P].add);
    Add(P<<1|1,mid+1,node[P].r,node[P].add);
    node[P].add=0;
    if(R<=mid)  return Query(P<<1,L,R);
    else if(L>mid)  return Query(P<<1|1,L,R);
    else return Query(P<<1,L,mid)+Query(P<<1|1,mid+1,R);
}
int main()
{
    int n,m,i;
    int a,b,c;
    char s[10];
    while(~scanf("%d%d",&n,&m))
    {
        for(i=1;i<=n;i++)
        {
            scanf("%d",&q[i]);
        }
        Build(1,1,n);
        for(i=0;i<m;i++)
        {
            scanf("%s",s);
            if(s[0]=='C')
            {
                scanf("%d%d%d",&a,&b,&c);
                Add(1,a,b,c);
            }
            else
            {
                scanf("%d%d",&a,&b);
                cout<<Query(1,a,b)<<endl;
            }
        }
    }
    return 0;
}