Snuke lives in another world, where slimes are real creatures and kept by some people. Slimes come in N colors. Those colors are conveniently numbered 1 through N. Snuke currently has no slime. His objective is to have slimes of all the colors together.

Snuke can perform the following two actions:

* Select a color i (1≤i≤N), such that he does not currently have a slime in color i, and catch a slime in color i. This action takes him a_i seconds.

* Cast a spell, which changes the color of all the slimes that he currently has. The color of a slime in color i (1≤i≤N-1) will become color i+1, and the color of a slime in color N will become color 1. This action takes him x seconds.




Find the minimum time that Snuke needs to have slimes in all N colors.

Constraints

* 2≤N≤2,000
* a_i are integers.
* 1≤a_i≤10^9
* x is an integer.
* 1≤x≤10^9

Input

The input is given from Standard Input in the following format:


N x
a_1 a_2 ... a_N


Output

Find the minimum time that Snuke needs to have slimes in all N colors.

Examples

Input

2 10
1 100


Output

12


Input

3 10
100 1 100


Output

23


Input

4 10
1 2 3 4


Output

10
header_code = """
#include "/opt/ac-library/atcoder/internal_bit.hpp"
#include "/opt/ac-library/atcoder/lazysegtree.hpp"
#include "/opt/ac-library/atcoder/modint.hpp"
#include <vector>
#include <algorithm>
#include <cassert>

namespace aclython {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    segtree(int n) : segtree(std::vector<S>(n, e())) {}
    segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = atcoder::internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    template <bool (*f)(S)> int max_right(int l, S b) {
        return max_right(l, b, [](S x, S y) { return f(x, y); });
    }
    template <class F> int max_right(int l, S b, F f) {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]), b)) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]), b)) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r, S b) {
        return min_left(r, b, [](S x, S y) { return f(x, y); });
    }
    template <class F> int min_left(int r, S b, F f) {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm), b)) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm), b)) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};



int min_op(int n, int m){
    return std::min(n, m);
}

int min_e(){
    return (int)1e9;
}

struct segtree_min {
    public:
        segtree_min() : segtree_min(0) {}
        segtree_min(int n) : segtree_min(std::vector<int>(n, min_e())) {}
        segtree_min(const std::vector<int>& vec) : seg(vec) {}

        void set(int p, int x) {seg.set(p, x);}
        int get(int p) {return seg.get(p);}
        int prod(int l, int r) {return seg.prod(l, r);}
        int all_prod() {return seg.all_prod();}

        int max_right(int l, int v) {return seg.max_right(l, v, [](int x, int y) { return x<y; });}
        int min_left(int r, int v) {return seg.min_left(r, v, [](int x, int y) { return x<y; });}

    private:
        segtree<int, min_op, min_e> seg;
};

int max_op(int n, int m){
    return std::max(n, m);
}

int max_e(){
    return 0;
}

struct segtree_max {
    public:
        segtree_max() : segtree_max(0) {}
        segtree_max(int n) : segtree_max(std::vector<int>(n, max_e())) {}
        segtree_max(const std::vector<int>& vec) : seg(vec) {}

        void set(int p, int x) {seg.set(p, x);}
        int get(int p) {return seg.get(p);}
        int prod(int l, int r) {return seg.prod(l, r);}
        int all_prod() {return seg.all_prod();}

        int max_right(int l, int v) {return seg.max_right(l, v, [](int x, int y) { return x<y; });}
        int min_left(int r, int v) {return seg.min_left(r, v, [](int x, int y) { return x<y; });}

    private:
        segtree<int, max_op, max_e> seg;
};

using mint = atcoder::modint998244353;

struct S {
    mint a;
    int size;
    S(mint _a, int _size) : a(_a) ,size(_size) {}
    S(int _a, int _size) : a(_a) ,size(_size) {}
    S(const S &s) : a(s.a), size(s.size) {}
    int get_a() { return (int)a.val(); }
};

struct F {
    mint a, b;
    F(mint _a, mint _b) : a(_a), b(_b) {}
    F(int _a, int _b) : a(_a), b(_b) {}
    F(const F &f) : a(f.a), b(f.b) {}
    int get_a() { return (int)a.val(); }
    int get_b() { return (int)b.val(); }
};

S op(S l, S r) { return S{l.a + r.a, l.size + r.size}; }

S e() { return S{0, 0}; }

S mapping(F l, S r) { return S{r.a * l.a + r.size * l.b, r.size}; }

F composition(F l, F r) { return F{r.a * l.a, r.b * l.a + l.b}; }

F id() { return F{1, 0}; }

struct lazy_segtree{
    lazy_segtree() : lazy_segtree(0) {}
    lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    lazy_segtree(const std::vector<S>& vec) : seg(vec) {}
    void set(int p, S x) { seg.set(p, x); }
    S get(int p) { return seg.get(p); }
    S prod(int l, int r) { return seg.prod(l, r); }
    S all_prod() { return seg.all_prod(); }
    void apply(int p, F f) { seg.apply(p, f); }
    void apply(int l, int r, F f) { seg.apply(l, r, f); }
    private:
        atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> seg;
};

}
"""

code = """

# distutils: language=c++
# distutils: include_dirs=[/home/USERNAME/.local/lib/python3.8/site-packages/numpy/core/include, /opt/ac-library]
# cython: boundscheck=False
# cython: wraparound=False

from libcpp cimport bool
from libcpp.vector cimport vector
cdef extern from "./intermediate.hpp" namespace "aclython" nogil:
    cdef cppclass segtree_min:
        segtree_min(vector[int] v)
        void set(int p, int x)
        int get(int p)
        int prod(int l, int r)
        int all_prod()
        int max_right(int l, int v)
        int min_left(int r, int v)

cdef class SegTreeMin:
    cdef segtree_min *_thisptr
    def __cinit__(self, vector[int] v):
        self._thisptr = new segtree_min(v)
    cpdef void set(self, int p, int x):
        self._thisptr.set(p, x)
    cpdef int get(self, int p):
        return self._thisptr.get(p)
    cpdef int prod(self, int l, int r):
        return self._thisptr.prod(l, r)
    cpdef int all_prod(self):
        return self._thisptr.all_prod()
    cpdef int max_right(self, int l, int v):
        return self._thisptr.max_right(l, v)
    cpdef int min_left(self, int r, int v):
        self._thisptr.min_left(r, v)

cdef extern from "./intermediate.hpp" namespace "aclython" nogil:
    cdef cppclass segtree_max:
        segtree_max(vector[int] v)
        void set(int p, int x)
        int get(int p)
        int prod(int l, int r)
        int all_prod()
        int max_right(int l, int v)
        int min_left(int r, int v)

cdef class SegTreeMax:
    cdef segtree_max *_thisptr
    def __cinit__(self, vector[int] v):
        self._thisptr = new segtree_max(v)
    cpdef void set(self, int p, int x):
        self._thisptr.set(p, x)
    cpdef int get(self, int p):
        return self._thisptr.get(p)
    cpdef int prod(self, int l, int r):
        return self._thisptr.prod(l, r)
    cpdef int all_prod(self):
        return self._thisptr.all_prod()
    cpdef int max_right(self, int l, int v):
        return self._thisptr.max_right(l, v)
    cpdef int min_left(self, int r, int v):
        self._thisptr.min_left(r, v)


def SegTree(v, op):
    if op=="min":
        return SegTreeMin(v)
    elif op=="max":
        return SegTreeMax(v)

cdef extern from *:
    ctypedef long long ll "long long"

cdef extern from "./intermediate.hpp" namespace "aclython" nogil:
    cdef cppclass S:
        S(int, int)
        S(S &)
        int get_a()
        int size
    cdef cppclass F:
        F(int, int)
        F(F &)
        int get_a()
        int get_b()
    cdef cppclass lazy_segtree:
        lazy_segtree(vector[S] v)
        void set(int p, S x)
        S get(int p)
        S prod(int l, int r)
        S all_prod()
        void apply(int p, F f)
        void apply(int l, int r, F f)

cdef class LazySegTree:
    cdef lazy_segtree *_thisptr
    def __cinit__(self, vector[vector[int]] v):
        cdef int n = v.size()
        cdef vector[S] *sv = new vector[S]()
        cdef S *s
        for i in range(n):
            s = new S(v.at(i).at(0), v.at(i).at(1))
            sv.push_back(s[0])
        self._thisptr = new lazy_segtree(sv[0])
    cpdef void set(self, int p, vector[int] v):
        cdef S *s = new S(v.at(0), v.at(1))
        self._thisptr.set(p, s[0])
    cpdef vector[int] get(self, int p):
        cdef S *s = new S(self._thisptr.get(p))
        cdef vector[int] *v = new vector[int]()
        v.push_back(s.get_a())
        v.push_back(s.size)
        return v[0]
    cpdef vector[int] prod(self, int l, int r):
        cdef S *s = new S(self._thisptr.prod(l, r))
        cdef vector[int] *v = new vector[int]()
        v.push_back(s.get_a())
        v.push_back(s.size)
        return v[0]
    cpdef vector[int] all_prod(self):
        cdef S *s = new S(self._thisptr.all_prod())
        cdef vector[int] *v = new vector[int]()
        v.push_back(s.get_a())
        v.push_back(s.size)
        return v[0]
    cpdef void apply(self, int p, vector[int] v):
        cdef F *f = new F(v.at(0), v.at(1))
        self._thisptr.apply(p, f[0])
    cpdef void apply_range(self, int l, int r, vector[int] v):
        cdef F *f = new F(v.at(0), v.at(1))
        self._thisptr.apply(l, r, f[0])
"""


import os, sys, getpass

if sys.argv[-1] == 'ONLINE_JUDGE':
    code = code.replace("USERNAME", getpass.getuser())
    open('intermediate.hpp','w').write(header_code)
    open('atcoder.pyx','w').write(code)
    os.system('cythonize -i -3 -b atcoder.pyx')
    sys.exit(0)


from atcoder import SegTree

N,x = list(map(int,input().split()))
A = list(map(int,input().split()))
ST = SegTree(A,"min")
ans = 10**27
for i in range(N):
    t = 0
    for j in range(N):
        if j-i<0:
            t += min(ST.prod(0,j+1),ST.prod(N+j-i,N))
        else:
            t += ST.prod(j-i,j+1)

    ans = min(t+i*x,ans)

print(ans)